StarMath functions chart.rtf

{\rtf1\adeflang1025\ansi\ansicpg1252\uc1\adeff0\deff0\stshfdbch0\stshfloch31506\stshfhich31506\stshfbi31506\deflang1033\deflangfe1033\themelang1033\themelangfe0\themelangcs0{\fonttbl{\f0\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\f34\fbidi \froman\fcharset0\fprq2{\*\panose 02040503050406030204}Cambria Math;}
{\f36\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0302020204030204}Calibri Light;}{\f37\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0502020204030204}Calibri;}{\f40\fbidi \fmodern\fcharset0\fprq1{\*\panose 020b0609020204030204}Consolas;}
{\flomajor\f31500\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\fdbmajor\f31501\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\fhimajor\f31502\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0302020204030204}Calibri Light;}{\fbimajor\f31503\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\flominor\f31504\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\fdbminor\f31505\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\fhiminor\f31506\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0502020204030204}Calibri;}{\fbiminor\f31507\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\f41\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\f42\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\f44\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\f45\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\f46\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\f47\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\f48\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\f49\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\f381\fbidi \froman\fcharset238\fprq2 Cambria Math CE;}
{\f382\fbidi \froman\fcharset204\fprq2 Cambria Math Cyr;}{\f384\fbidi \froman\fcharset161\fprq2 Cambria Math Greek;}{\f385\fbidi \froman\fcharset162\fprq2 Cambria Math Tur;}{\f388\fbidi \froman\fcharset186\fprq2 Cambria Math Baltic;}
{\f389\fbidi \froman\fcharset163\fprq2 Cambria Math (Vietnamese);}{\f401\fbidi \fswiss\fcharset238\fprq2 Calibri Light CE;}{\f402\fbidi \fswiss\fcharset204\fprq2 Calibri Light Cyr;}{\f404\fbidi \fswiss\fcharset161\fprq2 Calibri Light Greek;}
{\f405\fbidi \fswiss\fcharset162\fprq2 Calibri Light Tur;}{\f408\fbidi \fswiss\fcharset186\fprq2 Calibri Light Baltic;}{\f409\fbidi \fswiss\fcharset163\fprq2 Calibri Light (Vietnamese);}{\f411\fbidi \fswiss\fcharset238\fprq2 Calibri CE;}
{\f412\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}{\f414\fbidi \fswiss\fcharset161\fprq2 Calibri Greek;}{\f415\fbidi \fswiss\fcharset162\fprq2 Calibri Tur;}{\f418\fbidi \fswiss\fcharset186\fprq2 Calibri Baltic;}
{\f419\fbidi \fswiss\fcharset163\fprq2 Calibri (Vietnamese);}{\f441\fbidi \fmodern\fcharset238\fprq1 Consolas CE;}{\f442\fbidi \fmodern\fcharset204\fprq1 Consolas Cyr;}{\f444\fbidi \fmodern\fcharset161\fprq1 Consolas Greek;}
{\f445\fbidi \fmodern\fcharset162\fprq1 Consolas Tur;}{\f448\fbidi \fmodern\fcharset186\fprq1 Consolas Baltic;}{\f449\fbidi \fmodern\fcharset163\fprq1 Consolas (Vietnamese);}{\flomajor\f31508\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\flomajor\f31509\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\flomajor\f31511\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\flomajor\f31512\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}
{\flomajor\f31513\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\flomajor\f31514\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\flomajor\f31515\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}
{\flomajor\f31516\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fdbmajor\f31518\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fdbmajor\f31519\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
{\fdbmajor\f31521\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fdbmajor\f31522\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fdbmajor\f31523\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\fdbmajor\f31524\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fdbmajor\f31525\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fdbmajor\f31526\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}
{\fhimajor\f31528\fbidi \fswiss\fcharset238\fprq2 Calibri Light CE;}{\fhimajor\f31529\fbidi \fswiss\fcharset204\fprq2 Calibri Light Cyr;}{\fhimajor\f31531\fbidi \fswiss\fcharset161\fprq2 Calibri Light Greek;}
{\fhimajor\f31532\fbidi \fswiss\fcharset162\fprq2 Calibri Light Tur;}{\fhimajor\f31535\fbidi \fswiss\fcharset186\fprq2 Calibri Light Baltic;}{\fhimajor\f31536\fbidi \fswiss\fcharset163\fprq2 Calibri Light (Vietnamese);}
{\fbimajor\f31538\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fbimajor\f31539\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\fbimajor\f31541\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}
{\fbimajor\f31542\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fbimajor\f31543\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\fbimajor\f31544\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}
{\fbimajor\f31545\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fbimajor\f31546\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\flominor\f31548\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\flominor\f31549\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\flominor\f31551\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\flominor\f31552\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}
{\flominor\f31553\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\flominor\f31554\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\flominor\f31555\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}
{\flominor\f31556\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fdbminor\f31558\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fdbminor\f31559\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
{\fdbminor\f31561\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fdbminor\f31562\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fdbminor\f31563\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\fdbminor\f31564\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fdbminor\f31565\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fdbminor\f31566\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}
{\fhiminor\f31568\fbidi \fswiss\fcharset238\fprq2 Calibri CE;}{\fhiminor\f31569\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}{\fhiminor\f31571\fbidi \fswiss\fcharset161\fprq2 Calibri Greek;}{\fhiminor\f31572\fbidi \fswiss\fcharset162\fprq2 Calibri Tur;}
{\fhiminor\f31575\fbidi \fswiss\fcharset186\fprq2 Calibri Baltic;}{\fhiminor\f31576\fbidi \fswiss\fcharset163\fprq2 Calibri (Vietnamese);}{\fbiminor\f31578\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\fbiminor\f31579\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\fbiminor\f31581\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fbiminor\f31582\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}
{\fbiminor\f31583\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\fbiminor\f31584\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fbiminor\f31585\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}
{\fbiminor\f31586\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}}{\colortbl;\red0\green0\blue0;\red0\green0\blue255;\red0\green255\blue255;\red0\green255\blue0;\red255\green0\blue255;\red255\green0\blue0;\red255\green255\blue0;
\red255\green255\blue255;\red0\green0\blue128;\red0\green128\blue128;\red0\green128\blue0;\red128\green0\blue128;\red128\green0\blue0;\red128\green128\blue0;\red128\green128\blue128;\red192\green192\blue192;
\caccentone\ctint255\cshade191\red46\green116\blue181;\red5\green99\blue193;\red149\green79\blue114;\red43\green145\blue175;\red163\green21\blue21;}{\*\defchp \f31506\fs22 }{\*\defpap \ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 }\noqfpromote {\stylesheet{\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 \snext0 \sqformat \spriority0 Normal;}{\s1\ql \li0\ri0\sb240\sl259\slmult1\keep\keepn\widctlpar\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\itap0 \rtlch\fcs1 
\af0\afs32\alang1025 \ltrch\fcs0 \fs32\cf17\lang1033\langfe1033\loch\f31502\hich\af31502\dbch\af31501\cgrid\langnp1033\langfenp1033 \sbasedon0 \snext0 \slink15 \sqformat \spriority9 \styrsid13714745 heading 1;}{\*\cs10 \additive 
\ssemihidden \sunhideused \spriority1 Default Paragraph Font;}{\*\ts11\tsrowd\trftsWidthB3\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblind0\tblindtype3\tsvertalt\tsbrdrt\tsbrdrl\tsbrdrb\tsbrdrr\tsbrdrdgl\tsbrdrdgr\tsbrdrh\tsbrdrv 
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af31506\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 \snext11 \ssemihidden \sunhideused 
Normal Table;}{\*\cs15 \additive \rtlch\fcs1 \af0\afs32 \ltrch\fcs0 \fs32\cf17\loch\f31502\hich\af31502\dbch\af31501 \sbasedon10 \slink1 \slocked \spriority9 \styrsid13714745 Heading 1 Char;}{\*\cs16 \additive \rtlch\fcs1 \af0 \ltrch\fcs0 \ul\cf18 
\sbasedon10 \ssemihidden \sunhideused \styrsid8740849 Hyperlink;}{\*\cs17 \additive \rtlch\fcs1 \af0 \ltrch\fcs0 \ul\cf19 \sbasedon10 \ssemihidden \sunhideused \styrsid8740849 FollowedHyperlink;}{\*\ts18\tsrowd\trbrdrt\brdrs\brdrw10 \trbrdrl
\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidthB3\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblind0\tblindtype3\tsvertalt\tsbrdrt\tsbrdrl\tsbrdrb\tsbrdrr\tsbrdrdgl\tsbrdrdgr\tsbrdrh\tsbrdrv 
\ql \li0\ri0\widctlpar\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 \sbasedon11 \snext18 \spriority39 \styrsid13714745 
Table Grid;}}{\*\pgptbl {\pgp\ipgp0\itap0\li0\ri0\sb0\sa0}}{\*\rsidtbl \rsid748623\rsid3831403\rsid4001539\rsid7434202\rsid7999950\rsid8258661\rsid8272348\rsid8740849\rsid8929195\rsid9570426\rsid12286619\rsid12416751\rsid13003868\rsid13714745\rsid14228063
\rsid14449958\rsid14747802\rsid15296841\rsid16129675}{\mmathPr\mmathFont34\mbrkBin0\mbrkBinSub0\msmallFrac0\mdispDef1\mlMargin0\mrMargin0\mdefJc1\mwrapIndent1440\mintLim0\mnaryLim1}{\info{\author Matt Campbell}{\operator Matt Campbell}
{\creatim\yr2014\mo11\dy16\hr9\min54}{\revtim\yr2014\mo11\dy16\hr10\min33}{\version3}{\edmins39}{\nofpages5}{\nofwords1007}{\nofchars5746}{\nofcharsws6740}{\vern57437}}{\*\xmlnstbl {\xmlns1 http://schemas.microsoft.com/office/word/2003/wordml}}
\paperw15840\paperh12240\margl1440\margr1440\margt1440\margb1440\gutter0\ltrsect 
\widowctrl\ftnbj\aenddoc\trackmoves0\trackformatting1\donotembedsysfont1\relyonvml0\donotembedlingdata0\grfdocevents0\validatexml1\showplaceholdtext0\ignoremixedcontent0\saveinvalidxml0\showxmlerrors1\noxlattoyen
\expshrtn\noultrlspc\dntblnsbdb\nospaceforul\formshade\horzdoc\dgmargin\dghspace180\dgvspace180\dghorigin1440\dgvorigin1440\dghshow1\dgvshow1
\jexpand\viewkind1\viewscale80\pgbrdrhead\pgbrdrfoot\splytwnine\ftnlytwnine\htmautsp\nolnhtadjtbl\useltbaln\alntblind\lytcalctblwd\lyttblrtgr\lnbrkrule\nobrkwrptbl\snaptogridincell\allowfieldendsel\wrppunct
\asianbrkrule\rsidroot8740849\newtblstyruls\nogrowautofit\usenormstyforlist\noindnmbrts\felnbrelev\nocxsptable\indrlsweleven\noafcnsttbl\afelev\utinl\hwelev\spltpgpar\notcvasp\notbrkcnstfrctbl\notvatxbx\krnprsnet\cachedcolbal \nouicompat \fet0
{\*\wgrffmtfilter 2450}\nofeaturethrottle1\ilfomacatclnup0\ltrpar \sectd \ltrsect\lndscpsxn\linex0\endnhere\sectlinegrid360\sectdefaultcl\sectrsid8740849\sftnbj {\*\pnseclvl1\pnucrm\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl2
\pnucltr\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl3\pndec\pnstart1\pnindent720\pnhang {\pntxta .}}{\*\pnseclvl4\pnlcltr\pnstart1\pnindent720\pnhang {\pntxta )}}{\*\pnseclvl5\pndec\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl6
\pnlcltr\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl7\pnlcrm\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl8\pnlcltr\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl9\pnlcrm\pnstart1\pnindent720\pnhang 
{\pntxtb (}{\pntxta )}}\ltrrow\trowd \irow0\irowband0\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar\s1\ql \li0\ri0\sb240\keep\keepn\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\pararsid13714745\yts18 \rtlch\fcs1 \af0\afs32\alang1025 
\ltrch\fcs0 \fs32\cf17\lang1033\langfe1033\loch\af31502\hich\af31502\dbch\af31501\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dbch\af0\insrsid15296841\charrsid13714745 Basic Arithmetic\cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\dbch\af0\insrsid15296841 Example usage}{\rtlch\fcs1 \af0 \ltrch\fcs0 \dbch\af0\insrsid15296841\charrsid13714745 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow0\irowband0\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow1\irowband1\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv
\brdrs\brdrw10 \trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid14228063\charrsid8740849 multiply(}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid13714745 integer/scalar/}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid8740849 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid14228063\charrsid13714745 /matrix, integer/scalar/}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid8740849 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid13714745 /matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid14228063\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid8740849 Multiplies all elements of a 1D}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid14228063\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid8740849 array with the}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid13714745  scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid14228063\charrsid8740849 .}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid14228063\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 A.multiply(x);}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid14228063\charrsid13714745 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid14228063\charrsid13714745 \trowd \irow1\irowband1\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 divide(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 scalar)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841 Divides all elements of}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849  }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 an }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 array by the}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 .}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 A.divide(3.0);}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow2\irowband2\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 add(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 /matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Adds arrays A and B}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 A.add(B);}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow3\irowband3\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 subtract(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 /matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Subtracts one vector (B) from the other (A). C = A - B.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 
A.subtract(B);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 
\ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow4\irowband4\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow5\irowband5\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842
\pard\plain \ltrpar\s1\ql \li0\ri0\sb240\keep\keepn\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\pararsid15296841\yts18 \rtlch\fcs1 \af0\afs32\alang1025 \ltrch\fcs0 
\fs32\cf17\lang1033\langfe1033\loch\af31502\hich\af31502\dbch\af31501\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dbch\af0\insrsid15296841\charrsid13714745 Vector Multiply\cell \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow5\irowband5\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842
\row \ltrrow}\trowd \irow6\irowband6\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 dotProduct(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 The dot product of the two 1D}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 vectors A and B}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 v1.dotProduct(v2);}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow6\irowband6\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 crossProduct(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 The cross product of two -precision vectors}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 A and B}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 v1.crossProduct(v2);}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow7\irowband7\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 crossProduct2(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 The cross product of two}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 vectors}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 A and B}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 which are of length}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 2. In actuality}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 there is no cross-product for 2D. Th}{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 is is shorthand for 2D systems }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 that are really simplifications of 3D. The returned scalar is actually the }{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849  in the third (read: z) direction.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid8272348 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348  z = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid8272348 StarMath}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 .crossProduct2(v1, v2);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow8\irowband8\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 multiplyVectorsIntoAMatrix(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Multiply vector by transpose of another vector to create a matrix.}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Product of each element of array-1 (1D ) with each element of array-2 (1D )}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 C[i}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 j] = A[i] * B[j]}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid8272348 double}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 [,] A = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid8272348 StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8272348 
.multiplyVectorsIntoAMatrix(v1, v2);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 
\af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow9\irowband9\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl
\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 EltMultiply(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 /matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 The element-by-element }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 (Hadamard) multiplication }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 of }{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vectors or matrices.\cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid8929195 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8929195 
[] v3 = v1.EltMultiply(v2);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 
\af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow10\irowband10\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl
\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow11\irowband11\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842
\pard\plain \ltrpar\s1\ql \li0\ri0\sb240\keep\keepn\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\pararsid13714745\yts18 \rtlch\fcs1 \af0\afs32\alang1025 \ltrch\fcs0 
\fs32\cf17\lang1033\langfe1033\loch\af31502\hich\af31502\dbch\af31501\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dbch\af0\insrsid15296841\charrsid13714745 Advanced Matrix Manipulation\cell \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15296841\charrsid13714745 \trowd \irow11\irowband11\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842
\row \ltrrow}\trowd \irow12\irowband12\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Singular}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 Scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Decomposition(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Computes the singular }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849  decomposition of A.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid8929195\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid12416751 [] sigma = M.SingularValueDecomposition();}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751 or}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid8929195 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8929195 [,] U, V;}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid8929195 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8929195 
[] sigma = M.SingularValueDecomposition(}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid8929195 out}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8929195  U, }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid8929195 out}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid8929195  V);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow12\irowband12\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow13\irowband13\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvmgf\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid12416751\charrsid8740849 GetEigen}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid13714745 Scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 s(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid12416751\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid12416751\yts18 {\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 
Gets the eigen}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751 values}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849  for matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid13714745 , }{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 A.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 var}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid12416751  eigenVectors = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751  }{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751 [size][];}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 
\af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 var}{\rtlch\fcs1 \af444\afs19 \ltrch\fcs0 \f444\fs19\cf1\highlight8\insrsid12416751  \'eb = A.GetEigenValuesAndVectors(}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid12416751 out}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751  eigenVectors);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid12416751\charrsid13714745 \trowd \irow13\irowband13\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvmgf\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow14\irowband14\ltrrow\ts18\trgaph108\trleft-108\trbrdrt
\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvmrg\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid12416751\charrsid8740849 GetEigen}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid13714745 Scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 sAndVectors(matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid12416751\charrsid13714745 )\cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 Gets the eigen}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid13714745 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid12416751\charrsid8740849 s and eigenvectors for matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 A.}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid12416751\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid12416751\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid12416751\charrsid13714745 \trowd \irow14\irowband14\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvmrg\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow15\irowband15\ltrrow\ts18\trgaph108\trleft-108\trbrdrt
\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 inverse(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Inverses the matrix A only i}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 f the diagonal is all non-zero. }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 A[i}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 i] != 0.0}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 double}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751 [,] B = A.inverse();}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow15\irowband15\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 LUDecomposition(matrix\cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Returns the LU decomposition of A in a new matrix.}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid12416751\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 double
}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751 [,] L, U;}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid12416751 
StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751 .LUDecomposition(A, }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 out}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid12416751  L, }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 out}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751  U);}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow16\irowband16\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 transpose(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Transposes the matrix}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 A.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid12416751 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751 [,] At = A.transpose();}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15296841\charrsid13714745 \trowd \irow17\irowband17\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 determinant(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Returns the determinant of matrix}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 A.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12416751 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12416751  detA = A.determinant();}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell 
}\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow18\irowband18\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 solve(matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Solves }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 for x given }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 , A, vector, b & perhaps an initial guess for x in the formulation: Ax = b\cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid748623 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid748623 [] x = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid748623 StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid748623 .solve(A, b);}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow19\irowband19\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow20\irowband20\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842
\pard\plain \ltrpar\s1\ql \li0\ri0\sb240\keep\keepn\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\pararsid13714745\yts18 \rtlch\fcs1 \af0\afs32\alang1025 \ltrch\fcs0 
\fs32\cf17\lang1033\langfe1033\loch\af31502\hich\af31502\dbch\af31501\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dbch\af0\insrsid15296841\charrsid13714745 Sizing and Finding\cell \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow20\irowband20\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842
\row \ltrrow}\trowd \irow21\irowband21\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Max(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Finds the maximum }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849  in the given array}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  and optionally returns}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 
 the row and column indices along with it.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid12286619\yts18 {
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 int}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619  rowIndex, colIndex;}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619  max = A.Max(}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 out}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619  rowIndex, }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 out}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619  colIndex);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow21\irowband21\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 Min}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 (vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell Finds the min}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 imum }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849  in the given array}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  and optionally returns}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849  the row and column indices along with it.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 
var}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619  min = v1.Min(}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 out}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid12286619  index);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow22\irowband22\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 find(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 scalar)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Finds all the indices for the specified find }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 scalar}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 .}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid12286619 List}{\rtlch\fcs1 
\af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 <}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 int}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 > indices = v1.find(100.0);}
{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow23\irowband23\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 norm1(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Returns to 1-norm (sum of absolute }{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 s of all terms)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 of the }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vector or matrix. Or with two arguments, find the norm2 of their difference.\cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid12286619 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619  diff = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid12286619 StarMath}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 .norm1(v1, v2);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow24\irowband24\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 norm2(}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vector/}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Returns to 2-norm (square root of the sum of squares of all ter}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 ms) of the vector or matrix (optionally can choose to not do the square root). Or with two arguments, find the norm2 of their difference.\cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid12286619\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid12286619 [,] A;}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 ...}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 A.norm2();}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15296841\charrsid13714745 \trowd \irow25\irowband25\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 normP(}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vector/}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Returns to p-norm (p-root of the sum of each term raised to the p power)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid12286619\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid12286619 double
}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 [,] A;}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 ...}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid12286619 A.normP(10.0);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell 
}\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow26\irowband26\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7434202\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid7434202 normalize}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid8740849 (}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid13714745 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid8740849 )
}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202 Returns the}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid7434202  normalized vector (has leng}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202 t}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid7434202 h }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202 (}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid7434202 
or 2-norm}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid7434202  of 1) of the vector, x.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid13714745 \cell }{\rtlch\fcs1 
\af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 [] v1;}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 
\af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 ...}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 v1 = v1.normalize();}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid7434202\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7434202\charrsid13714745 \trowd \irow27\irowband27\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid7999950\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 normalizeInPlace(}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Destructively normalize}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 s}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849  the vector x.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\faauto\rin0\lin0\pararsid7434202\yts18 {\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 [] v1;}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 ...}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 v1.normalizeInPlace();}{\rtlch\fcs1 
\af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid15296841\charrsid7434202 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 
\ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow28\irowband28\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 sum(}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vector/matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Sum up all the elements of a given }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vector or }{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7434202\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 var}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid7434202  v1 = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 [] \{ 1, 2, 3, 4, 5 \};}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 var}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202  avg = v1.sum() / 5.0;}{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow29\irowband29\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 standardDeviation(}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 vector/}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Calculates the standard deviation assuming the whole population is provided (not sample st. dev.).}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7434202\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 var}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202  v1 = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 [] \{
 1, 2, 3, 4, 5 \};}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 var}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid7434202  stdev = v1.standardDeviation();}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow30\irowband30\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow
}\trowd \irow31\irowband31\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar\s1\ql \li0\ri0\sb240\keep\keepn\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\pararsid15296841\yts18 \rtlch\fcs1 \af0\afs32\alang1025 
\ltrch\fcs0 \fs32\cf17\lang1033\langfe1033\loch\af31502\hich\af31502\dbch\af31501\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dbch\af0\insrsid15296841\charrsid13714745 3D Coordinate Transforms\cell \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15296841\charrsid13714745 \trowd \irow31\irowband31\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow32\irowband32\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv
\brdrs\brdrw10 \trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Translate(scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 scalar)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Creates a translated coordinate frame.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [,] t = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid9570426 StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 
.Translate(1.2, 3.4, 5.6);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 
\af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow32\irowband32\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl
\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 RotationX(scalar)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Creates a rotation matrix about the X-axis.}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid7434202 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 [,] rx45 = }{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid7434202 StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 .RotationX(45.0);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 
\cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 
\af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow33\irowband33\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 RotationY(scalar)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Creates a rotation matrix about the Y-axis.}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7434202\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid7434202 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 [,] ry90 = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid7434202 StarMath}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 .RotationY(90.0);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow34\irowband34\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 RotationZ(scalar)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Creates a rotation matrix about the Z-axis.}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid7434202\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid7434202 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 [,] rz30 = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid7434202 StarMath}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid7434202 .RotationZ(30.0);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow35\irowband35\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow
}\trowd \irow36\irowband36\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar\s1\ql \li0\ri0\sb240\keep\keepn\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\pararsid15296841\yts18 \rtlch\fcs1 \af0\afs32\alang1025 
\ltrch\fcs0 \fs32\cf17\lang1033\langfe1033\loch\af31502\hich\af31502\dbch\af31501\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dbch\af0\insrsid15296841\charrsid13714745 Make/Get/Set Methods\cell \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15296841\charrsid13714745 \trowd \irow36\irowband36\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7507\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\trowd \irow37\irowband37\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv
\brdrs\brdrw10 \trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid9570426\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 makeZero(integer}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid9570426 , integer}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 {\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 
Makes the zero vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 /matrix of the given dimensions}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 .}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\faauto\rin0\lin0\pararsid9570426\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [] g = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid9570426 StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 .makeZeroVector(3);}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [,] H = }{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid9570426 StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 .makeZero(4,3);}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid15296841\charrsid9570426 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow37\irowband37\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 makeIdentity(integer)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Makes an identity matrix of size p by p.}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 var}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426  I = }{\rtlch\fcs1 
\af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid9570426 StarMath}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 .makeIdentity(4);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell 
}\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 
\ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow38\irowband38\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 makeLinearProgression(scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 scalar}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 scalar)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Makes a linear progression from start to}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 but not including}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 the end.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 
\af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [] timeSteps = }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf20\highlight8\insrsid9570426 StarMath}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 .makeLinearProgression(100, 0.01);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow39\irowband39\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 SetRow(integer}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Sets/Replaces the given row of matrix A with the vector v.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid9570426\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 A.SetRow(0, }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid9570426 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [] \{ 1.0, 2.0, 3.0 \});}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15296841\charrsid13714745 \trowd \irow40\irowband40\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 SetColumn(integer}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 Sets/Replaces the given column of matrix A with the vector v.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid9570426 A.SetColumn(0, }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [] \{ 1.0, 2.0, 3.0 \});}{\rtlch\fcs1 
\af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow41\irowband41\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 GetColumn(matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 integer)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Gets the column of matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 A.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid9570426 [] trans = A.GetColumn(4);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow42\irowband42\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 GetColumns(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Get more than one column from a given 2D}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 array.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [,] rotation = A.GetColumns(}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [] \{ 0, 1, 2 \}
);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow43\irowband43\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 GetRow(integer}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Gets a row of matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 A.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid9570426 [] scale = A.GetRow(4);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow44\irowband44\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 GetRows(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Get more than one row from a given 2D}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 
\ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 array.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid9570426\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid9570426 [,] rotation = A.GetRows(}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [] \{ 0, 1, 2 \});}{
\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow45\irowband45\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 GetPartialVector(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Get some portion of a vector and put in a new vector.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell 
}\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid9570426\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid9570426 [] rx = col.GetPartialVector(}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid9570426 new}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid9570426 [] \{ 0, 1, 2 \});}{
\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 
\f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow46\irowband46\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 JoinCol(matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell J}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 o}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 i}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 ns two 2D }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 
 arrays side by side and returns the results. The given variables remain unchanged}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\faauto\rin0\lin0\pararsid14747802\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid14747802 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid14747802 
[,] AB = A.JoinCol(B);}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid15296841\charrsid14747802 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 \trowd \irow47\irowband47\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 JoinRow(matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Joins two 2D }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849  arrays one under the other and returns the results. The given variables remain unchanged}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid14747802 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid14747802 [,] AB = A.JoinRow(B);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar
\ql \li0\ri0\sa160\sl259\slmult1\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid15296841\charrsid13714745 \trowd \irow48\irowband48\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 JoinVectors(vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 vector)}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 Concatenates two 1D}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745  }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 arrays and returns the result. The given variables remain unchanged}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid14747802\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid14747802 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid14747802 [,] v12 = v1.JoinVectors(v2);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow49\irowband49\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 JoinMatrixColumnsIntoVector(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 
Joins the matrix columns into vector.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\faauto\rin0\lin0\pararsid14747802\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf2\highlight8\insrsid14747802 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid14747802 [,] A; }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid14747802 ...}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid3831403 \line }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid14747802 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid14747802 [] Avect = A.JoinMatrixColumnsIntoVector();}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid15296841\charrsid14747802 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow50\irowband50\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 JoinMatrixRowsIntoVector(matrix)}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 
Joins the matrix rows into vector.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 \cell }{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf2\highlight8\insrsid14747802 double}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf1\highlight8\insrsid14747802 [] Avect = A.JoinMatrixRowsIntoVector();}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
\trowd \irow51\irowband51\ltrrow\ts18\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth3\trwWidth12950\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddft3\trpaddfb3\trpaddfr3\tblrsid14228063\tbllkhdrrows\tbllkhdrcols\tbllknocolband\tblind0\tblindtype3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth4135\clshdrawnil \cellx4027\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row \ltrrow}\pard\plain \ltrpar
\ql \li0\ri0\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\pararsid13003868\yts18 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid8740849 MakePrintString(matrix}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid13714745 , vector}{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid15296841\charrsid8740849 )}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\f37\cf1\insrsid15296841\charrsid13714745 \cell Makes the string printing the matrix or vector\cell }\pard \ltrpar\ql \li0\ri0\widctlpar\intbl\wrapdefault\faauto\rin0\lin0\pararsid14747802\yts18 {\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 
\f40\fs19\cf20\highlight8\insrsid14747802 Console}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid14747802 .WriteLine(}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf21\highlight8\insrsid14747802 "A = "}{\rtlch\fcs1 \af40\afs19 
\ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid14747802 + A.MakePrintString());}{\rtlch\fcs1 \af40\afs19 \ltrch\fcs0 \f40\fs19\cf1\highlight8\insrsid15296841\charrsid14747802 \cell }\pard\plain \ltrpar\ql \li0\ri0\sa160\sl259\slmult1
\widctlpar\intbl\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \rtlch\fcs1 \af0\afs22\alang1025 \ltrch\fcs0 \f31506\fs22\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid15296841\charrsid13714745 
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\cltxlrtb\clftsWidth3\clwWidth3372\clshdrawnil \cellx7399\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth5443\clshdrawnil \cellx12842\row }\pard \ltrpar
\ql \li0\ri0\widctlpar\tx5506\wrapdefault\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid13714745 {\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid3831403 \line }{\rtlch\fcs1 \af0 \ltrch\fcs0 \f37\cf1\insrsid8258661\charrsid8740849 
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