Chapter 15 - Innear Product and Orthogonality.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import scipy as sp\n",
    "import scipy.linalg\n",
    "import scipy.spatial\n",
    "import sympy as sy\n",
    "sy.init_printing() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Dot Product</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider two vectors\n",
    "\n",
    "$$\n",
    "\\mathbf{u}=\\left[\\begin{array}{l}\n",
    "u_{1} \\\\\n",
    "u_{2} \\\\\n",
    "\\vdots \\\\\n",
    "u_{n}\n",
    "\\end{array}\\right] \\quad \\text { and } \\bf{v}=\\left[\\begin{array}{l}\n",
    "v_{1} \\\\\n",
    "v_{2} \\\\\n",
    "\\vdots \\\\\n",
    "v_{n}\n",
    "\\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dot product of $\\mathbf{u}$ and $\\mathbf{v}$,i.e. $\\mathbf{u}\\cdot\\mathbf{v}$ is defined as\n",
    "\n",
    "$$\n",
    "\\left[\\begin{array}{llll}\n",
    "u_{1} & u_{2} & \\cdots & u_{n}\n",
    "\\end{array}\\right]\\left[\\begin{array}{c}\n",
    "v_{1} \\\\\n",
    "v_{2} \\\\\n",
    "\\vdots \\\\\n",
    "v_{n}\n",
    "\\end{array}\\right]=u_{1} v_{1}+u_{2} v_{2}+\\cdots+u_{n} v_{n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can generate two random vectors, then let's compare operations in NumPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.round(100*np.random.randn(10))\n",
    "v = np.round(100*np.random.randn(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -846., -1700., -6486., -1886., -1100.,  6776., -6210.,  1586.,\n",
       "        -245.,  2394.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u*v # this is element-wise multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -7717.0$"
      ],
      "text/plain": [
       "-7717.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u@v # matrix multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -7717.0$"
      ],
      "text/plain": [
       "-7717.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.inner(u,v) # inner product here is the same as matrix multiplication"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SymPy operation is the same like in linear algebra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = sy.randMatrix(1, 10)\n",
    "v = sy.randMatrix(1, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}15991\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[15991]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u*v.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Norm of a Vector</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The <font face=\"gotham\" color=\"red\">norm</font> is the length of a vector, definted by\n",
    "\n",
    "$$\n",
    "\\|\\mathbf{v}\\|=\\sqrt{\\mathbf{v} \\cdot \\mathbf{v}}=\\sqrt{v_{1}^{2}+v_{2}^{2}+\\cdots+v_{n}^{2}}, \\quad \\text { and } \\quad\\|\\mathbf{v}\\|^{2}=\\mathbf{v} \\cdot \\mathbf{v}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A NumPy built-in ```np.linalg.norm()``` is for computing norms.The default setting is to compute the length of vectors from origins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 6.324555320336759$"
      ],
      "text/plain": [
       "6.324555320336759"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [2, 6]\n",
    "np.linalg.norm(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verify the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 6.324555320336759$"
      ],
      "text/plain": [
       "6.324555320336759"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(2**2 + 6**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also compute a group of vectors' length, for instance $(2, 6)^T$, $(8, 2)^T$, $(9, 1)^T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.32455532, 8.24621125, 9.05538514])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[2, 8, 9], \n",
    "              [6, 2, 1]])\n",
    "np.linalg.norm(A, axis = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Distance in $\\mathbb{R}^n$</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $\\mathbf{u}$ and $\\mathbf{v}$ in $\\mathbb{R}^{n}$, the distance between $\\mathbf{u}$ and $\\mathbf{v},$ written as dist $(\\mathbf{u}, \\mathbf{v}),$ is the length of the vector $\\mathbf{u}-\\mathbf{v} .$ That is,\n",
    "\n",
    "$$\n",
    "\\operatorname{dist}(\\mathbf{u}, \\mathbf{v})=\\|\\mathbf{u}-\\mathbf{v}\\|\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have two vectors $\\mathbf{u} = (2, 9)$ and $\\mathbf{v} = (-3, 4)$, compute the distance and visualize the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 7.0710678118654755$"
      ],
      "text/plain": [
       "7.0710678118654755"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = np.array([2, 9])\n",
    "v = np.array([-3, 4])\n",
    "np.linalg.norm(u - v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Err4aevVy7efl+bFo0QXX5RARcVIQFhGRYpn95Wzu+vQuZwgO8g+ide3WbJm+hdqhtUvW2Jo1rlUwsrOhS5cy1zdggDUhRaHkZPj4Yy22ISIXpyAsIiKX9dq213jw8wfdQvDVda8mYWoCNYNrlqyxrCxrEuBC7dpZvcJl5O8PY8daE1IU+u472LatzE2LSBWlICwiIpf04qYXeWzNY84QHOwIpnODzmy4YwPVg6qXvMEdO6yllAH8/GDgQI/VWq0ajBsHhmF1AwcEuE4lInI+TZ8mIiIX9cz6Z3h247Nk5Frz/YY4QujaqCsrb11JSEApE+bGja6llcPDoX9/D1VradYMIiNTMM0WjB8P9et7tHkRqUIUhEVEpAjTNHnyiyd5eevLbiG4d9PefDrpU4IcZZiod+VK111sWVnQs6cHKnbXvv0Zevf2yIgLEanCFIRFRMSNaZo8tvoxXt/xulsIvq7FdXx484cE+AeUpXFraEShunWhdglvtCsGw1AIFpHL0xhhERFxMk2TBz57wC0EhwaEMrTVUJZNWFa2EAzWTXLnTuPQr1/Z2iuhnBw4fLhCTykiXkxBWEREACgwC5j28TTmfT3PLQTf1OYmFo9bjMPPAx8inruscliYR2+Uu5zkZJg1C955x31ROxHxXQrCIiJCfkE+kz+czKLvF7mF4Jvb38y7o9/F38/fMydavRrS0137566CUY4OH7ZCcHKyNSx50SLIza2QU4uIF1MQFhHxcXkFedz8wc0s+3GZWwie0mkKc0bMwc/w4K+KDRtc24YBrVt7ru1LqF/fGo5c6Ngx+OyzCjm1iHgxBWERER+Wm5/LyIUj+WzvZ24h+J7Ie3h12KsYhuG5k506BcePu/a7drXCcAVwOGD8eAgNdR376iv48ssKOb2IeCkFYRERm8TGxmIYhvMRExNDYmKi2zHDMIiNjS2X82fnZXPD+zfwxf4vnItlhAaE8vvuv+eFQS94NgQDbNoEwcHWdmAgDB7s2fYvo0YNGDPGPXt/9hkcPVqhZYiIF1EQFhGxSWxsLKZpOh9xcXFERka6HTNNs1yCcGZuJoPeHcTGXze6heDHez/O3wf83fMhGGDdOjh71toODoY+fTx/jsu48kqIjnbt5+VZ44UzMyu8FBHxAgrCIiI+Jj0nnevevo5th7c5Q3CII4S/Rv+Vv/T/S/mdePVq19RpmZnW0Agb9OsHV13l2k9NhQ8/dJ/VTUR8g4KwiIgPOZN9hn7z+vHV0a/IyrOWOQ5xhPDcwOd4tNej5XfinBz44QfX/lVXuYZJVDDDgNGjoWZN17E9e9zv4xMR36AgLCLiI1KzUun9Vm++P/492fnZgBWCZw6dyQPdHijfk+/cCUG/LctsGDBgQPme7zJCQqyb5/zPmRUuLg5++sm+mkSk4ikIi4j4gJMZJ+kxuwd7Tu5xC8Fv3vgm06+dXv4FbNxo9QoDVKsGMTHlf87LaNQIhg1z7ZsmLF0K2dn21SQiFUtBWESkijuefpxus7vxc8rP5ORbYTTEEcK8kfO4tdOtFVPEypWuhJmdXWELaVzOtddC587WdnAwjBjh6rgWkarPA+tlioiItzpy9gg9Z/fkSNoR8gryACsELxyzkBFtR1RMEaYJW7e69mvWtFa48AKGATfcAAUF1mwSERF2VyQiFUlBWESkijp4+iA9ZvcgKT2JfDMfsELw0vFLGXrV0Ior5MAB17AIsGXatEsJCLBunhMR36MgLCJSBe1P2U+POT04mXHSGYJDA0L5ZOInXNfiuootJiHBdVdaaCgMGlSx5xcRuQiNERYRqWL2ntxL1KwoTmSccIbgsIAwVt66suJDMMDatZCWZm37+XnN+ODLycyE5ct185xIVaYeYRGRKmRX8i76vNWH1KxUTKwVIsIDw1kzeQ3dm3S3p6j4eNd2fj5cfbU9dZTAkSOweLG12EZ6Oowb5740s4hUDeoRFhEpgd27d9O5c2fno3r16rz88stur4mPj6dGjRrO18yYMaNCavsm6Rt6zelFSlaKMwRXD6rOutvX2ReCT5+Gw4dd+126WL3CXqygAD74wArBALt2wZYt9tYkIuVDPcIiIiXQpk0bdu7cCUB+fj6NGzdm1KhRRV7Xt29fPv300wqrK/FIIjHzYzibc9Z5rGZQTdbfsZ4O9TtUWB1FbNlirV6RmwsOBwwZYl8txeTnB6NGwdy5VigGa3XoRo2gWTN7axMRz/LuP8tFRLzY2rVrufLKK2lmczracmgL0fOjnSHYwCAiJILN0zfbG4IB1q+3xhaAdaOcl80YcTFNm8Lgwa79ggJYssQ11FlEqgYFYRGRUlq4cCETJ0684HObN2+mU6dODB06lO+//77I84ZhFHnExMSQmJh4wecuZv0v67n+7etJy7ESmp/hR+3Q2mydvpW2ddp65o2WxapV1rhgsO4+69bN3npKoFs3uOYa135amhWGC3uJRaTyM0zTLJeGly9fboaFhZVL274oLS2N8PBwu8uoEnQtPceXr2Vubi5jx45l7ty5RJy3CkN6ejp+fn6EhISwZcsW/vOf//Duu++6vSamhEsMx8XFFTl2Nvss+1L2UWC6klmAXwBt67Ql0D+wRO2Xmy+/tBbUAGvJtnOTZTny1Pdmbq7Bp5825PRp1/W85prTdO2aUua2Kwtf/nfuabqWnnXu9YyOji7V7azlFoTj4+PN6OjocmnbF8XHx6Pr6Rm6lp7jy9fyo48+4tVXX2XVqlWXfW3z5s3ZsWMHderUueTr4uPjefTRR9mxY8dl21y+ZznjPxhPRm4GAA4/B/XD6rNl+haaVG9SvDdR3r76Cvr3h7O/jVu++254440KObUnvzeTk2HWLPc1QW6+Gdq180jzXs+X/517mq6lZ513PUsVhDU0QkSkFBYsWHDRYRHHjh2jsJNh27ZtFBQUULt2bY+de9mPyxi3ZJxbCG5crTHb79zuPSEYYONG6yY5gGrV4Dob5jD2gLp1YcR5q1EvWwYnT9pTj4h4joKwiEgJZWRksHr1akafsy7vG2+8wRu/9XZ+8MEHXHPNNXTq1IkHH3yQhQsXXnKcb0ks/G4hk5ZOIjMvE7CGQjSv2Zztd26nYbWGHjmHx6xcCVlZ1nZubqVZSONCrrkGevRw7Wdnw6JF7r3EIlL5aPo0EZESCg0N5eR53YH33HOPc/uBBx7ggQce8Ph53975Nvcsv8cZggP9A2lZqyUJUxOICIm4zFfb4NzJd8PCoIkX9VaXwsCB1pTIBw9a+8nJsH8/tGljb10iUnrqERYRqQTeTHzTLQQH+QfRtk5btkzb4p0h+NAh17RpUKl7gwv5+1srzIWFWY/JkxWCRSo79QiLiHi5mVtn8viax50hONgRTPu67YmbEke1oGo2V3cRCQkQEGANjQgOhkGD7K7II6pXh4kTrf9Wr253NSJSVgrCIiJe7PmE53k6/mm3ENylQRfW3LaG0IBQm6u7hLg412wRAQHQu7e99XhQJR/hISLnUBAWEfFSM9bN4J8J/3SG4BBHCN0bd+fzWz8n2BFsc3WXsXatazsnBzrYvMJdBShcaMNPgw5FKg39cxUR8TKmafLEmif4Z8I/nVOkhThC6NesHysnr/T+EJyWBr/84trv2BEcVbvf5exZmD8f1q2zuxIRKYmq/ZNJRKQSenjlw8z6cpYzBIcGhDKgxQCWjl9KgH+AzdUVw7ZtEBJiTZnm719lxgdfzC+/WEsvF+b/Jk3gqqvsrkpEikM9wiIiXuSX078UCcE3XHUDH978YeUIwQAbNkCGVT9hYdCvn731lLOUFCsEF/rf/yA11b56RKT4FIRFRLxAgVnAgdQDnMo45RaCR7cdzcKxC/H387e5whJYuRLy8qztzEz3lSiqoM6dITLStZ+ZCYsXuy6BiHgvBWEREZvlF+QzaekkUrJSKDCtO65CA0KZ1GES80fNx8+oRD+qCwpg507XfpMmPjHP2NCh0PCchf2OHIHPP7evHhEpnkr001VEpOrJK8hjzOIxfLL7E7cQPLXzVN688c3KFYIBdu2yxgUXio62rZSK5HDA+PHW0OhCiYnufxOIiPepZD9hRUSqjpz8HEYsGMGqn1aRkWcNh/Az/Lg/6n5mDp2JYRg2V1gKGze65hELD4cBA+ytpwLVqgWjR7sf+/RTOHbMnnpE5PIUhEVEbJCVl0WbMW34/NbPyXwyE2Lh0UmPUnCkgOcHPY+fnx+GYWAYBrGxsXaXW3yrV7tulMvPr1ILaRTHVVdB//6u/bw8a7xwVpZ9NYnIxWn6NBGRCpaRm8HgdwaTFJUEXaxjIY4Q3ur0Fi/EvsCOHTvsLbAsEhJc24GB0KyZfbXYpH9/OHQIfvrJ2j91Cj78ECZMgMrYyS9SlalHWESkAqXlpBEzL4YdR3a4rRj39wF/p0F4A5urK6OkJPd5w3r08Mnk5+cHY8ZAjRquY7t3u/+NICLeQUFYRKSCnMk+Q9+5ffk66Wuy8q3PykMcIbw46EUe7vGwzdV5QEICBAVZ20FBMHiwvfXYKDTUunmu8L5Bf3/XpRER76GhESIiFSAlM4W+c/uy79Q+svOzASsEvzrsVe7ocofN1XlIfLy11jBYwyJ8bHzw+Ro3hiFDrPVFxo+3ZpITEe+iICwiUs5OZJyg91u9OZB6gJz8HMAKwbNHzGZSh0k2V+dBa9aAaVrb2dnQpYu99XiBrl2hY0f1Bot4KwVhEZFylJSWRM85PTl05hC5BbmAFYLfHf0uo9uNvsxXVyKZmbBvn2v/6qshoJIsCV2ODEMhWMSbaYywiEg5OXzmMF1ndeXgmYNuIXjx2MVVKwSDtXpE4WoSfn5w/fX21uPl8vLg8GG7qxARBWERkXLwS+ovRM2K4ujZo+QV5AEQ6gjlw5s/5MY2N9pcXTnYsMHqFQZrIQ0fWVGuNFJSYM4cmD8fkpPtrkbEtykIi4h42E+nfiJqVhRJ6Unkm/mAtWzy8luWM7hVFZ1JYeVKyLV6vcnMhJ497a3HSx0/Dm++CUePQk4OLFpkDacWEXsoCIuIeNDuE7vpNrsbJzJOUGBaSw2HBYSxevJqoptH21tceTFNOHcRkPr1ISLCvnq8WJ06UK+ea//ECfjkE9c9hiJSsRSERUQ85Pvj39NjTg9SMlMwsZJNtcBqxE2Jo1fTXjZXV4727HHf79fPnjoqAT8/GDvWGj1S6LvvYNs2+2oS8WUKwiIiHrDz2E56vdWL1KxUZwiuHlSd9XesJ6pxlM3VlbNzl0wLC4OBA+2rpRKoVg3GjbNCcaGVK+HgQftqEvFVCsIiImW0/fB2+s3tx5nsMwAYGNQMrsmmqZvo3KCzzdVVgNWrIT3d2jZNn19IoziaNXOfWKOgABYvdl1GEakYCsIiImWw6eAmYubHcDbHWlHNwCAiJIKt07fSvl57m6urIBs2uLb9/aFVK/tqqUR69oR27Vz7Z8/CBx9YoVhEKoaCsIhIKa07sI6B7wwkPdfqxvMz/KgbVpdtd26jde3WNldXQU6edJ8DrGtXaxUJuSzDgJEjoXZt17H9+yEuzr6aRHyNgrCISCms2reKYe8PIyM3AwB/w5/6YfXZNn0bLWu1LFYbsbGxGIbhfMTExJCYmOh2zDAMYmNjy/GdlNGmTRAcbG0HBsKQIfbWU8kEBcHNN7svwrdhA/z4o301ifgSBWERkRL6dPenjFw00hmCHX4OGlZryPY7t9OsZrNitxMbG4tpms5HXFwckZGRbsdM0/TuILxunfWZPliBWOODS6xePRg+3P3YsmUaLyxSERSERURKYOkPSxn/wXgy86xV1AL8AmhavSk77txB4+qNba7OBqtXuybBzcyEyEh766mkOnaEbt2s7YAAGDrUmoBDRMqXw+4CREQqi/e/fZ/pH093huBA/0Ca1WjGpmmbqBNax+bqbJCT4/4ZfuvWrmESUmKDBll/S/TpY61JIiLlTz3CIuI1DMNg3rx5lz1mh7lfzXULwUH+QbSKaMXW6VsvGoK9+f14xFdfuYKvYcCAAfbWU8k5HDBmjEKwSEVSEBYRuYzXt7/O/Z/d7xaC29Vtx+Zpm6kVUsvm6my0cSNkZ1vb1apBTIy99YiIlJCCsIjIJfxry7/4w6o/OENwsEui3bQAACAASURBVCOYTg06seGODVQPqm5zdTZbscIVhLOyoFcVXkbaRjk51qXOzLS7EpGqR0FYRCqV6Oho57RixTleFs9ufJYnv3jSCsGfA7GQ9WQWz7V9jvDAcOfrunfvjmEYhIeHc7ZwBoWqzjRh+3bXfkSENf2BeFRyMsyaBVu2wP/+57ovUUQ8Q0FYROQCno57mmfWP+OcIi0oKsj53P+W/M+5/fPPP7Nt2zYAxo4dS7Vq1Sq2ULvs3w+5ua79Pn3sq6WKMk1rpbnC9Ur27oX16+2tSaSqURAWETmHaZr8cfUfeWHzC84QHOII4boe13Ft5LUALF68mPz8fADef/9959dOnTq14gu2S0IC+P32KyQ01JryQDzKMOCmm6yb6ArFx8NPP9lWkkiVoyAsIj5jzZo1RVZtO//h5+fHi3e/6AzBoQGhDGk1hI8nfsy0qdMAOHbsGHG/rYO7YMECAFq1akW/fv3seWN2WLMG0tKsbcPQ+OBy0qgRDBvm2jdNWLoUTp+2ryaRqkTzCItIlZCXl3fZ1/Tq1Ysffvjhgs8VmAU8Hf80n+75lCyyACsED289nPdGv4e/nz+TJk3iD3/4A1lZWbz//vvUrVuXXbt2AT7WGwzWinKFTBPatbOvliquSxc4eNCarQ4gIwMWL4Y77nDvLRaRktM/IRGpVIKCXGN1s7KyCA4OxjRN9u/ff9mvDQ0NpW3btkWOF5gF3L7sdj5L+Yysmq4QPO7qcbx101v4GdaHZzVr1mTkyJEsXLiQ//3vf9SoUQMAf39/pkyZ4om3VzmkpsKRI679Ll1cwyTE4wzD6hU+ehSOHbOOHT4MK1fCDTfYW5tIZaefXCJSqTRr1sy5/cknnwDwyiuvcOTcYFYC+QX5TPhgAkt/WOo2HGJyx8nMvWmuMwQXKuz5PX36NP/5z38AGDx4MI0aNSrV+SulLVsgJMTadjhgyBB76/EBAQEwfrz7wn3bt8M339hXk0hVoCAsIpXKLbfc4tweP3481apV46GHHiKkMJiVQG5+LqMWjWL53uVuIfjOa+/k9Rtev+BUbAMGDHCG8cLhGD43LGL9ekhPt7ZDQzVjRAWJiIBRo9yPffIJJCXZU49IVaAgLCKVSv/+/Zk9ezatW7cmKCiIK6+8kiVLltCtW7cStZOdl82NC25kzc9r3ELwg90e5F+D/3XR+Yj9/PzchkHUqVOHESNGlP4NVUarVsFvs2aQmQklvPZSem3aQN++rv3cXGu8cFaWfTWJVGYKwiJS6UybNo3du3eTlZXFzp07GTt2LPHx8ZimiVmMFQey8rIY/O5gNvyywbliXGhAKH/s9Ueevf7Zyy7K8de//tV5ruTkZAICAkr1PmJjY91mrIiJiSExMbHITBaxsbGlar9c5OXBd9+59lu0sHqFpcLExEDLlq79kydhzx776hGpzBSERcSnZORmcN3869h6eKtbCI7tH8vT0U9XaC2xsbHOQG2aJnFxcURGRrodM03Tu4LwN99AYKBr/7rr7KvFR/n5wZgxUL06BAXBhAnQsaPdVYlUTpo1QkR8xtnss8TMj+H75O/JyrM+Sw5xhPDsgGd5sPuDNldXSWzc6FpRrlo1BWGbhIVZATg42Bo7LCKloyAsIj7hdNZp+s3rx+4Tu8nOzwasEPzykJe5K/Ium6urRFatcg1Izc2F3r3trceH+dJEJSLlRUFYRLzGhcb3FmfM7+WcyjxFn7f68FPKT+Tk5wBWCH7jhje4rfNtZW7/Ysrr/dhq82bXdni40pgXMk3roamdRS5P/0xEpEpLTk+m++zu7Du1zy0Ezx05t1xDcJV08KC1rFkhLavsdTIz4f33rRWwReTy1CMsIlXWsbRj9JjdgyNnj5BbYI1rDXGE8P6Y9xnZdqTN1VVCCQnWyg5ZWdaCGoMG2V2RnOPIEWsqtdRU2LsXmjSBq6+2uyoR76YeYRGpkg6dOUTXN7ty+OxhZwgODQjlg3EfKASXVlwcnD1rbfv7a3ywl0lJsUJwoWXL4MQJ++oRqQwUhEWkyjmQeoCoN6M4lnaMvAJr9bfQgFA+uvkjhrUeZnN1ldjata7tvDzo0MG+WqSI9u2hRw/Xfk4OLFpk/VdELkxBWESqlH2n9hE1K4rjGcfJN63Vz8ICwvj8ls+5/srrba6uEktLg19/de137Gj1CotXGTgQrrjCtZ+cbC3DXNnv0RQpLwrCIlJl/HjiR7rN6sbJjJMUmAUAhAeGs+a2NfRr1s/m6iq5rVutccFgBWCND/ZK/v4wdqw1z3Chb7+F7dvtq0nEmykIi0iV8G3St/SY3YOUrBRMrO6v6oHViZ8ST48mPS7z1XJZGza4ZowIC4N++sPCW1WvboXhc1cKX7kSDh2yryYRb6UgLCKV3pdHv6TP3D6czj7tPFYjqAYbpm4gslGkjZVVIStXWuOCwZqjq4f+uPBmLVrAgAGu/fx8a0aJ9HT7ahLxRgrCIlKpbT20lf7z+nMm+wwABga1gmuxedpmOtbvaHN1VUR+Puzc6dpv2tRaXlm8Wu/e0Lata//MGVi6FAoK7KtJxNsoCItIpbXx140MeHsAaTlpAPgZftQOrc3W6VtpV7edzdVVIbt2geOcaeejo20rRYrPMGDkSIiIcB37+WeIj7etJBGvoyAsIpXS2p/XMvjdwaTnWp/1+hv+1A2ty7bp27iq9lU2V1fFbNxo9QqDtazyuZ+5i1cLDoabb7bWQQErHAcG2luTiDdREBaRSmfF3hUMXzCcjFzr5i2Hn4P64fXZfud2WtRqYXN1xRcbG4thGM5HTEwMiYmJbscMwyA2NtbeQlevtsYFgxWItZBGpVK/Ptx4o3WP4+TJ0KeP3RWJeA8FYRGpVD7+8WNGLx5NZp4VzBx+DhpVa8SOO3fQtEZTm6srmdjYWEzTdD7i4uKIjIx0O2aapv1BOCHBtR0U5D5RrVQKnTrB734HLVvaXYmId1EQFpFKY8muJUxYOsEZggP8AriixhVsv3M7Das1tLm6KurYMTjtmo2DHj3c5+WSSiM42O4KRLyPgrCIVArvfv0uUz6c4gzBgf6BtKzVkm3Tt1EvrJ7N1VVhCQlWLzBYSWrwYHvrEY8qKND8wuLbFIRFxOvN/nI2d316lzMEB/kH0bp2a7ZM30Lt0No2V1fFxcfD2bPWdkCAxgdXIWfPwvz5MG8eHD1qdzUi9lAQFhGv9uq2V3nw8wfdQnD7eu3ZNHUTNYNr2lydD1izBkxrpT6ys6FzZ3vrEY9ISYH//hd++cVaJ2XxYtf9kJdimiadOnVi/vz5AMybN6/IzZ2GYfDGG2+UqJ7itHP//fczbdq0ErUrcjmOy79ERMQeL2x6gafjn3aG4GBHMJ0bdGbN5DWEBYbZXJ0PyMyEn35y7bdv75qHSyq1GjWgQQPYt8/aT0mBZctgwoRLDwFfvHgxKSkpTJo0ye34F198QUhIiHO/ZSnvyrtUO4899hht27bliSeeoFWrVqVqX+R8CsIi4pWeWf8Mz2581jlFWogjhG6Nu/H5LZ8TEhByma8Wj9ixA0JCIDcX/Pxg4EC7KxIP8fOD0aOtXuHCeyF377amjO7b9+JfN3PmTCZPnkzAeX8QRUVFER4eXua6LtVO8+bN6dOnD6+//jovvvhimc8lAhoaISJexjRN/rz2z0VCcJ8r+rDy1pUKwRVpwwbX5+Xh4dC/v731iEeFhsL48eDv7zr2xRfW6nMXsm/fPjZt2sTYsWMrpsALGDNmDO+99x4FWidaPERBWES8hmmaPLb6MV7e+rIzBIc6QrmuxXUsn7ScIEeQzRX6mJUrrd5gsAJxz5721iMe17gxDB3q2jdNWLoUzpwp+tq1a9cSFhZGp06dijx35ZVX4nA4aNOmDf/9739LXc/l2unVqxdJSUl8++23pT6HyLk0NEJEvIJpmjzw2QPM+3qeKwQHhDK01VAWjl2Iw08/ripUQQEkJrr2GzSAWrXsq0fKTWQkHDwIX39t7aenw5IlcPvt7r3FiYmJtGvXDj8/Vx9aw4YN+dvf/ka3bt3Iz89nwYIF3HPPPWRkZPDwww8Xu4bittO+fXv8/f3Ztm3bBQO5SEnpN4uI2K7ALGD6x9NZ9P0itxA8su1I3h75Nv5+/pdpQTxuzx73fQ2LqLIMw1qC+dgxSEqyjh08CKtWufcWHzt2jDp16rh97eDBgxl8ztzSQ4cOJTs7m2eeeYaHHnrILTRfSnHbcTgc1KxZk2PHjpXy3Yq409AIEbFVfkE+kz+cXCQET2g/gXdGvaMQbJdzl1UOD4frr7evFil3AQHWeOGgc0Yfbd0K333n2s/KyiIo6PLDk8aOHcupU6c4cOBAmWq6WDtBQUFkZWWVqW2RQgrCImKbvII8bv7gZpb9uMwtBN/e6XZmj5iNn+GdP6KaN29Ohw4d6Ny5M127di3yvGmaPPjgg7Rq1YqOHTvy5Zdf2lBlGa1ebX1GDtYwCS2kUeXVrg0jR7of+/hjSEuz/hiNiIggNTW12O0ZHlqK+/x2UlNTiYiI8EjbIhoaISK2yM3PZdSiUXyx/wvnPMGhAaHc2/Venh/4vMd+iZaXuLi4Ih8TF/r888/Zu3cve/fuZevWrdx7771s3bq1gissow0bXNv+/nDllfbVIhWmXTvrb56EBOt/+8CBkJaWD0CbNm3YvHnzZdtYunQpderUoVmzZmWq5ULtJCcnk5GRQevWrcvUtkghBWERqXDZedkMXzCcjb9udAvBD/d4mL/F/M3rQ/DlfPTRR9x2220YhkGPHj1ITU3l6NGjNGzY0PmaS73HCz1nFq7uVhFOnLAehaKiLr3KglQpAwZYyy936waNG5usW2cd7927NzNmzCA5OZm6desC1nRm3bp1o2PHjuTn57No0SIWLVrEzJkz3cYHx8fHExMTQ1xcHNHR0UXOWdx2duzYgWEY9OrVq1yvgfgOo7x+uC5fvtwMC9PKT56SlpbmkcnKRdfSk0pzLU3TZM+pPWTkZlBgWnOB+hl+NAxvSIPwBuVRpsdNnDiRatWqATB8+HCGDx/u9vwTTzzBpEmT6NChAwCPPPIId999N23atHG+JiYmpkTnjIuLK2PVJXD6NOzfD/n5VgBu3Bjq16+483uA/p2X3eq4cH49cZqrGgRxVSsHdeqcZezYsdx///0MGjQIgFmzZrFhwwaOHz+OaZo0a9aMsWPHOp8vtGXLFp544gnmzp1L8+bNi5yruO288sor/Pzzz/zrX/8qt/ddnvR96VnnXs/o6OjS/bVumma5POLi4kzxHF1Pz9G19JySXsu07DSz+6zuZvAzwSaxmMRihv491Hxx04vlU2A5OXz4sGmappmUlGR27NjRXLdundvzw4YNMzds2ODcv+6668wdO3Zctt24uDgzMjLSs8WWxiOPmKafn2mCaVavbpoJCXZXVGL6d156h88cNkcvHG1ydxfTf/xE8667d5vvv2899+CDD5rDhg0rcZtPPfWUGR0dXaa68vLyzMaNG5vvvPNOmdqxk74vPeu861mqvKqhESJSIc5knyF6XjS7kneRnZ8NWCvGPX/989zX7T6bqyuZRo0aAVCvXj1GjRrFtm3b6Nevn/P5Jk2acPDgQef+oUOHnF9TKaxebd0gB9ZCGpGR9tYjFSIrL4vnE57nHwn/ICc/h+CmDmbcNpGu2Ufo3dsak/vYY4/Rpk0b9uzZU6Jxups2beKRRx4pU31LliwhJCSECRMmlKkdkXN55y3ZIlKlpGal0vut3kVC8CvDXql0ITg9PZ2zZ886t1etWsU111zj9poRI0bw9ttvY5omW7ZsoUaNGm7jg71adjbs3u3ab9PGfU4tqXJM0+TDHz6k+cvN+cfGf5CRm0FeQR5Nqzfl4R4PYxgQGGi9tkmTJsyZM4ejR4+W6ByrV68uMoSoNHXOmTMHh0N9eOI5+m4SkXJ1MuMkvd/qzf7U/eTk5wBWCH7zxje5tdOtNldXcklJSYwaNQqAvLw8Jk2axJAhQ3jjjTcAuOeeexg2bBifffYZrVq1IjQ0lLlz59pZcsl89RUEB0NOjjU+WPMHV2m7kncx/ePpfJ30tXMKQ7D+jb4z6p0LruhoV4/sxIkTbTmvVG0KwiJSbo6nH6fnnJ4cPH2Q3IJcwPoFO3/UfMZdPc7m6kqnZcuWfF24Fu057rnnHue2YRi8+uqrFVmW52zcCIWLFVSrBhe4w18qv5TMFB5f+zhvf/022XnZmLhunA/yD2LCNRPo3qS7jRWKVAwFYREpF0fOHqHn7J4cSTtCXkEeYIXghWMWMqLtCJurk4taudLqDQYrEGuaqiolvyCfNxPf5P/W/B85+TnOoUrnCjLC+H/9X7KhOpGKpyAsIh538PRBeszuQVJ6EvmmNRl/iCOE/43/H0OuGmJzdXJRpgnbtrn2a9eG3+aLlcpv/S/rmfbxNA6dOURWXhZB/kXHfocFhBHbeS7//XdN6tWDpk0BtMy5VF26WU5EPGp/yn66zurqFoJDA0JZPmm5QrC3+/lnyMtz7ffpY18t4jG/nv6V4e8Pp/+8/uw7tY/c/NwLvs7P8KNj/Y50Ch6OaUJSEuzYYa0wJ1JVKQiLiMfsPbmXqFlRnMg44QzBYQFhrLx1JTEtSraAhNggIQEKV/EKDYXzFjOQyiUzN5Mnv3iSVjNb8eneT+lYvyPPDniWJtWbEOQf5BwWEehvTQkR5B/E/JHzOXTItS5BRASEhOTbUr9IRdDQCBHxiF3Ju+jzVh9Ss1KdN96EB4az9ra1dGvczebqpFjWroW0NGvbMKB3b3vrkTL5/Yrfs+qnVfy575+5rdNtVA+qTu+3enM07ahzBpdg/2Ac/g4choNHej7ClbWuYskhVxvW0AiRqktBWETK7Jukb+g3tx+ns087j1UPqk78lHi6NOxiY2VSIvHxrm3TtOYQlkrr5SEvE+wIxjAMjqcfp/vs7vx6+le3GVwC/AM4k32GxtUa82S/J0lKct0rCVYQLvzbSKQq0tAIESmTxCOJ9HmrjzMEGxjUDKpJwtQEheDKJDUVzl0k4dprXcMkpFIKCQjBMAyOnj1K1Kwofjn9izMEhwaE8srQV0jLSSPAL4B3Rr1DkCOIcxZEBOCKK2woXKQC6aeciJRaem460fOiOZtjrbRmYFArpBabp2/mmnrXXOarxats3gwhIdZ2QAAM0Y2NVcHB0weJmhXFkbOuaQxDA0L5YNwHpGSlUGAWMKLNCOcY/nODcHCwJg2Rqk9DI0SkVNb/sp49J/eQlmt9bupn+FE7pDabp23myogrba5OSmz9etdn4CEhmjGiCtifsp+ec3oWuXn1owkfcV2L67h3+b2EBoTy2g2vOb/m119dX9+kiTVUXKQqU4+wiJTY6p9WM/S9oRSYBQD4G/7UC6vH9ju3KwRXVqtWQYH1/5PMTIiKsrceKZO9J/fSbXY3kjOS3ULwiltXMKDlAHYc2cEvp3/hpUEvUS+sHgBnzsBp1zB/DYsQn6AeYREpkeV7ljP+g/Fk5GYA4PBz0CCsAZunb6ZJ9SY2VyelkpsL333n2m/Z0po+TSqlH5J/oPdbvYvM4LJm8hrnssmv7XiNzvU7c2fknc6vO398sGaMEF+gHmERKbZlPy5j3JJxzhBsYNC4WmO237VdIbgUYmNjMQzD+YiJiSExMdHtmGEYxMbGlm8h33wDQeesMjZgQPmeT8rNN0nf0HNOT1KyUpwhuHpQddbdvs4ZggEahDXg7VFv42e4YsC5wyL8/KBx4worW8Q2CsIiUiwLv1vIpKWTyMzLBCDAL4BA/0C237mdBuENbK6ucoqNjcU0TecjLi6OyMhIt2OmaZZ/EN640eoVBqhWDWK0+ElllHgkkb5v9XWbxrBGUA023rGRaxte6/baZ69/lg71O7gdO7dHuH59CAws13JFvIKGRojIZb29823uWX6PMwQH+gdyZa0raVe3HXXDdFt5pbdyJWRlWds5OdCrl731SIltObSFge8MJC3HuuHRwKBmsDWNYbu67S779aYJLVpYPcFHj2p8sPgOBWERuaQ3E9/k9yt+7wzBQf5BtKnThvW3r+erLV/ZXJ14xJYtru3q1aFRI/tqkRLb8MsGhr43lPTcdMCawSUiJILN0zbTKqJVsdowDBg40NrOzXV9QCBS1WlohIgAYJomnTp1Yv78+c5jM7fOdAvBwY5gOtTvwMY7NlIjuEaRNj744AN69epF7dq1CQ4Opk2bNjzzzDPknLtUVQkcPnyY8PBwDMMg7bzlre6//36mTZtWqnblHL/+as0SUUi9wZXKmp/WMOS9Ic4Q7G/4Uy/UmsGluCH4fAEBuldSfIeCsIgAsHjxYlJSUpg0aRIAzyc8z+NrHncLwdc2vJZ1t6+jWlC1C7Zx8uRJYmJimD17Np9//jlTp07l73//O4888kipanrssccIDw+/6HPvvfce+/btK1Xb8puEBCv5gDV/8KBB9tYjxfbZns+4adFN7jO4hDdg+13baV6zub3FiVQSGhohIgDMnDmTyZMnExAQwF/X/ZXnEp5zhuAQRwg9mvTgs1s+I9gRfNE27r77brf9mJgYzpw5w6uvvsorr7yCUYLZ+Tds2MCKFSv405/+xGOPPVbk+ebNm9OnTx9ef/11XnzxxWK3K+f54gs4a60MiL8/9O5tbz1SLMt+XOZ286rDz0Hjao3ZPG0zDas1tLk6kcpDPcIiwr59+9i0aRNjxozhiTVP8FzCc85ephBHCP2a9WPFrSsuGYIvpnbt2iUeGpGfn8/vfvc7nnrqKerUqXPR140ZM4b33nuPgsKFIKTk4uJc23l5cI2WxvZ2i75fVGQGl+Y1m7P9zu2lCsH5+dbNciK+SEFYRFi7di1hYWHMPzafmdtmOkNwaEAog64cxCcTPyHQv/hzKeXn55ORkcHGjRuZOXMm9957b4l6g9944w2ysrK4//77L/m6Xr16kZSUxLffflvstuUcZ8+6Tx7bqZPVKyxe6+2db3PHsjvcZ3CJuJKt07eWegaXnTvhuefgvfdgwwZr4hARX6EgLCLs2LGD0IahzN452y0E39j6RpaOX0qAf0CJ2gsLCyMsLIy+ffvSv39/nn/++WJ/7cmTJ/nLX/7CSy+9REDApc/bvn17/P392bZtW4nqk99s22aNCwZwOGDwYHvrkUua9eUst2kMg/yDaFunLVumbSEiJKLU7RbeL7l3rxWEHRo0KT5E3+4iPq7ALGDF1ys4aZykINcaYhAaEMrwK4bzVPun2Ltn70W/9tdzexPPsWnTJjIyMti2bRszZszggQce4LXXXitWPX/+85/p3r07w4YNu+xrHQ4HNWvW5NixY8VqW86zfj1kWH/4EBoKffvaW49c1MytM4vcvNq+bnvipsRd9ObV4jp3IY0mTay5hEV8hYKwiA/LL8jnlv/dwpGUIxT4u0LwLR1uIepYFO2vbn/ZNm677bYix6691lrFqk+fPtSpU4cpU6bwhz/8gSuvvPKSbX3//fe89dZbrF+/ntTUVAAyfgtqp0+fxt/fn5DCHszfBAUFkVW4GISUzMqV1rhgsLoEu3e/9OvFFs8nPM/T8U+7heAuDbqw5rY1hAaUbZ6ztDQ4dcq137RpmZoTqXQUhEV8VF5BHmMXj2X1T6spCCqANCsET+syjX8P+TeGYXDnnXdeso34+PjLnqcwFO/fv/+yQXjv3r3k5ubSs2fPIs81adKEadOmMXv2bLfjqampRESU/mNhn5WfD19/7dq/4gpreWXxKjPWzeCfCf90m8GlW+Nupb559Xzn9gaDVpQT36MgLOKDcvJzGLlwJPEH4q1fsHXAOGzwQNQD/OP6f5ToxrbLSUhIAKBFixaXfW2fPn2IO3cWA2DFihX885//5LPPPqNly5ZuzyUnJ5ORkUHr1q09Vq/P+P5798Gg0dG2lSJFmabJn9b+ye3m1RBHCH2b9eXjCR8T5AjyyHnODcKGAY0be6RZkUpDQVjEBz34+YPE7Y8jK98aUhDUIojsddk82vnRMoXgIUOGcP311ztvYktISODFF1/k5ptvdvYGx8fHExMTQ1xcHNHnha86deoUOXbgwAEA+vbtW2RxjR07dmAYBr20GlrJbdxo9QqD1RM8YIC99YiTaZo8suoR3kx803XzqiOUAS0HlOrm1Us5d5h/vXoQXPZOZpFKRUPiRXzQDVfdQH6BFXhDA0J58rYniYiIYMWKFWVqNyoqinnz5jFu3DjGjx/PJ598wrPPPss777zjfE3hmN969eqV6Vxg9Rb379+f2rVrl7ktn7NqlWtp5dxcLaThJUzT5N7l97qH4IBQbmh9Ax/e/KFHQ3BeHhw96trXsAjxRQrCIj5oeJvhDDy1FHJD6Jvzd/7U/0luvfVWFi5cWKZ2//a3v/Hdd9+RlpZGamoqX375Jb/73e/cpkHbunUr0dHRXH311cVq8/bbb8c0zSK9wfn5+SxdupRp06aVqWY7xcbGYhiG8xETE0NiYqLbMcMwiI2N9fzJN21ybYeE6C4pL1BgFjD1o6m88807biF4dNvRLBy7EH8/z87xfOSI60MB0LeA+CYFYREf9cqDQ/F7NoN1//w9Q4bA3Xc/Rnx8PHv27CnX827atIlHHnmkzO0sWbKEkJAQJkyY4IGq7BEbG4tpms5HXFwckZGRbsdM0/R8ED56FM6cce336GENEBXb5Bfkc8vSW1i8a7FbCJ7UYRLzR83Hz/D8r+vzZz9UEBZfpCAs4qNatoSYGMjKsqaTHTSoCX/96xyOnvtZaTlYvXo1w4cPL3M7pmkyZ84cHJr9v+QSEiDot5utgoO1kIbN8gryGLdkHB/v+dgtBE/tPJU3b3yzXEIwuN8oV60a1KxZLqcR8Wr6DSLiw/78Z9iyBdLT4fBhePrpCbz1lt1VFc/EiRPtLqHyio+3llcGCAjQ+GAbFZnBBSsE3xd1H89d/5xHZ3A5l2m6B+GmkzSA3gAAIABJREFUTfWhgPgm9QiL+LDoaOtO8UIZGTB1Kjz4oGudBamC1qyxkhBAdjZ06mRvPT4qOy+bYe8NKxKCH+35KM8PfL7cQjBATg60aOGaOlrDIsRXqUdYxIcZBvzpT/D731u9wmCF4TlzYOtW+PRTqFvX3hrFwzIy4OefXfvXXGP1CkuFysjNYPC7g0k8kugWgv/c98/8qe+fyv38QUEwbpz199Dp0/oWEN+lHmERH3fLLeB33k+CjAz46iu4+mrYvt2euqSc7NhhzRIB1v/4gQPtrccHpeWkETMvhh2Hd7hCsCOUZ657pkJC8LkMwxobHBZWoacV8RoKwiI+LiQE7r3Xde9UodxcOHEC+veH//7XntqkHGzY4Jo/ODzc+h8sFeZM9hn6zu3L10lfOxe0CXGE8MKgF3i4x8M2VyfiexSERYSHHrrwjTL+/tYQ0ocegttus7alklu50vorB6xA3LOnvfX4kJTMFHrN6cUPyT+QnW/9YwpxhPDqsFe5N+pem6sT8U0KwiJCo0YwaJAVhs8NxEFBVhjOz4d33oFrr3W/01wqmYICSEx07TdsqDmzKsiJjBP0mNODvaf2uoXg2SNmc0eXOyq0lsL7JEVEQVhEfvOnP1nDJAICXENIMzLA4YAZM6yhpLt2Qfv2EBdnb61SSrt3u/+lo2ERFSIpLYlus7qxP2U/Ofk5gBWC3xn9DpM6TKrweuLi4PXXrZthv/lGwVh8m4KwiADQvTs0b25Nq5SZCaGh1vHMTPh//8/6xbl1q3UD3fXXw3PP2VqulEZCgms7PNz6Hynl6vCZw0TNiuLgmYPkFlhDUkIcISweu5gx7cbYUtMvv0BSknXf5IYNmj9YfJuCsIg4PfkkBAZC9erQoYNrSqX0dBgyxJppa8sWWLXK6imWSmb1atc8eQUFWkijnP16+leiZkVx5OwR8gqsiblDA0L58OYPubHNjbbUlJ9vLZ5TSPMHi69TEBYRp7FjrWmUzpyBV15xTbZvmnDoENxxh7U9YAA88oi9tUopbNjg2vb3t9bZlnLxc8rPRM2KIik9iXwzH4CwgDCWT1rO4Fb2LWl99Kj7YjkKwuLrFIRFxCkgwFpcA+Cnn+CTT1zjhbOyrDGFmkqtkkpOhpMnXfvduukz8XKy5+Qeus3qRnJ6MgVmAWCF4FWTVxHdPNrW2s6/2fWKK+ypQ8RbKAiLiJv77rOGPcTFQa9e8MwzrvHCGRnwhz9YYwulktm0CYKDre3AQGusi3jc98e/p/vs7pzKPIWJdRdatcBqxE2Jo1fTXjZX5x6EQ0MhIsK+WkS8gYKwiLipUwfGj4d166z9hx+2hkIULriRkQE33ACnTtlXY1URGxuLYRjOR0xMDImJiW7HDMMgNja27Cdbtw7OnrW2g4I0Prgc7Dy2k15v9SI1K9UZgqsHVWf9HeuJahxlc3XWsKZff3XtN22qDwVEFIRFpIjHH7eGRmRkWL8o338f6td3/dJMTYVRo+ytsSqIjY3FNE3nIy4ujsjISLdjpml6JgivXu2aJys725oUWjxm++Ht9JvbjzPZZwAwMKgZXJOEqQl0btDZ5uosqamQluba17AIEQVhEbmADh3g669d44PDw60FyQr3c3Ks4RFHjthXo5RAdrY1h3ChNm2Krqktpbbp4CZi5sdwNsfqcTcwqBVSiy3TtnBNvWtsrs7l/PHBulFOREFYRC7i6qvdPzZt2xbmzHEfL5yUZAVk8XJffun6K8YwNH+wB607sI6B7wwkPdeals7P8KNOaB22Tf//7N13eFNl+wfw72nT3TILFCjDskEoL6UsAVtkL0FAEFkyXDgR9FVE4kBcqC8/FF8EFF4QFBBBRpmtyIaCqKgICgJlj0LbpPv5/fHQnIS2dCU5J8n3c125yElOTu4ckvbuk/u5n/1oFNpI4+hsWZdFeHvLFSWJPB0TYSIqtmHDgFGj1JwqN1fWE1v/giUd2rlTtv0AZE+8mBhNw3EXm09sRu+lvWHKMgEAvBVvVAuqhgMTDqBepXoaR5ef9YhwjRrsBU4EMBEmohKaPVt+s+7tLbfT0oDeveW376RTcXGyngWQCXEH7bsXuLp1x9Zh4NcDYcqWSbDBy4DqIdVxYMIB1KlQR+Po8ktPBy5dUrdZFkEkMREmohLx8ZH9hIOD5XZODvD337LtGumQEMCBA+p25cqyNQiV2re/f4sHVz5oSYJ9vHxQq1wtHJxwEDXL1dQ4uoKlpQE1a6p/wHKiHJHEL0aIqMRq1gRWrwZ++klum83A8uXAvffK0gnSkb/+kn+t5OncWbtY3MCyX5dh3JpxMGebAQC+3r6oU74Odo/bjdBA/f6BUbkyMH48kJUlJ7lWq6Z1RET6wBFhIiqV2FggLMx28twTTwC//KJtXHSbXbsAr1s/6oOCgG7dtI3HhX15+EubJNjP2w/1K9XHvvH7dJ0EW/PxAerUUddWIfJ0TISJqNSqV5flpr6+cttkAnr1Am7e1DYusrJtm23zWC6kUSqfHfgMT2540iYJblKlCfaM24OKARU1jo6ISouJMBGVyYoV8mvXPFeuAEOHqms3kMYSEtTrQgANG2oWiqv6eO/HeGHzC5Yk2N/bHy2qtcCPj/yIcn7lNI6OiMqCiTARlUmFCsDGjWqJREYGsGMH8M472sZFAK5fl82e87RurZZJULHM3DkTU7dPtUyMCzAEoHWN1kgYk4Bg32CNoyOisuJPRCIqs8hIYM4c23rhN98EfvhB27g83p49ajGojw/Qo4e28biY6fHT8daOtyx9ggMMAWgf3h5bRm1BoE+gxtEV37p1wNKlwI8/5l9djsjTMREmIrt45BFg0CB1sQ2zGRgwADh/Xtu4PNqOHWp9cEAA0LGjtvG4CCEEXtzyIj7Y84ElCQ40BOLeOvdi44iN8De41kyz48flZds2+ZYgIhUTYSKym3nz5Iz0vG/fU1OBPn1kyybSwObNcvk/QP5lEh2tbTwuQAiBZ+OexScHPlGTYJ9AdKvXDd8P/x6+3r4aR1gyN27ISx4upEFki4kwEdmNv7+sFw4KktvZ2cCxY8CkSdrG5ZGysoCjR9XtevXU4XoqUK7IxaPrHsWCwwtskuB+Dfth1YOrYPByvdb7t5dCMBEmssVEmIjsqm5dubhGXs5lMgELF8ruEmTLaDRCURTLJTY2FomJiTa3KYoCo9FY8oMfOQL4+cnrigLcd59dY3c3uSIXY74bg69++comCR7SdAi+GvQVvL28NY6wdKwTYS8vuRgOEamYCBOR3fXuDTz7rO3kuUcekaPDpDIajRBCWC7x8fGIioqyuU0IUbpEeOdOtSYlOFiugEIFysnNwbCVw7Dq91U2SfDIFiPxxf1fwEtx3V+V1olwWJja85uIJNf9dBORrr31FtCqlWxWAMhkuGdPIC1N27g8xqZNQHq6vJ6ZKVc+oXyycrIw6JtBWH98vU0SPKHVBMztMxeKomgcYellZgIXLqjbLIsgyo+JMBE5hLc3sHq17DMMyLUcLlwARo7kYhsOJwSwd6+6Xa6cXAaQbGTmZKLfsn7Y/NdmmyT4mTbP4KMeH7l0EgwASUnqXEkAqF1bu1iI9IqJMBE5TGgosH69Wi+cni4bGcyZo21cbu/0abmySR4uq5xPenY6eizpgR3/7LCsGBfoE4gXO7yImV1nunwSDMi3gTWOCBPlx0SYiBwqOhp4/321XjgtDXjpJWDfPm3jcmu7dgGGWx0OAgKA7t21jUdnTFkm3Lf4Puw9u9eSBAcYAvDava9hesx0jaOzH+v64AoV5BcDRGSLiTAROdyTTwK9eqmLnJnNQN++wOXL2sbltrZvB1JS5HVvby6kYSUlIwX3fnkvDp0/hPRsWUMdYAjAzK4z8dI9L2kcnf0IAZw9q25zNJioYEyEicjhFAVYvBioUUNeB2ST/wEDgJwcbWNzS/Hx6vXsbKBpU+1i0ZEb6TfQ8YuO+OXiLzZJ8Ec9P8KzbZ/VODr7unRJnSsJMBEmKgwTYSJyisBAIC5OLZHIygJ++gmYOlXbuNxOSortd+ItW8pRYQ93zXwN7Re0xx9X/kBGjqyfDjAEYG6fuXgs6jGNo7O/1FQgJETd5kQ5ooK53jI5ROSyGjSQI8MjRsjyCJMJmD1bfnPft6/W0bmJfftkXXBWlqwT7tFD64g0dzntMjos7IB/kv9BVq7srRxgCMDC+xdi2N3DNI7OMerVkys63rgh/y6qWlXriIj0iSPCRORUDzwATJigjgybzcDw4cDJk9rG5TZ27FCbNQcGAp06aRuPxi6kXkD059H5kuClDyx12yQ4j6LISXLNm8tV5YgoP340iMjpZs0CmjRRGxukpcnFNqxrGqmUNm1SC6/NZqBtW23j0dDZm2fRel5rJKUkWZLgQEMgVg5ZiYFNBmocHRHpARNhInI6gwFYt06tYczNlV/fjh+vbVxFOXPmDGJjY9GkSRM0a9YM//nPf/Ltk5CQgPLly6Nly5Zo2bIl3njjDecFmJMD/Pyzul27tlxe2QNl5mQi+vNoXEi9gOzcbACyT/CaYWvQu2FvjaMjIr1gjTARaSIsDFizRpawms3ysno1MH++fhNig8GAWbNmoVWrVkhJSUFUVBS6deuGprd1ZejUqRPWrVvn/AB//VUdZgeA2Fjnx6ADJ66dwO9XfseltEvIFXJptSCfIGx4eAM61+mscXREpCccESYizXTqBBiNar2wyQQ88wxw+LCmYRWqevXqaNWqFQAgJCQETZo0QVJSksZRWdm5Uy2LCAkB7rtP23g08MeVP9B2fltk52ZbkuBg32BsHbXVY5Lg1avlNy5HjgDJyVpHQ6RvTISJSFNTpgD33gv4+cltsxno3Ru4fl3buIpy6tQpHD58GG0LqMHds2cPIiMj0atXLxw9erTAxyuKku8SGxuLxMTEAu8rls2b5QkEZNcID1ta+ddLv6L9/Pa4Zr5muS3ENwQJoxPQLrydhpE5T1aW/GLg4EGZEO/apXVERPqmCCEccuD169eLoKAghxzbE6WmpiLYQ2v97I3n0n7sdS5zc+Uv7yw5nwmKIktbGzYs86Edwmw249lnn8WIESPQubPtKGNaWhq8vLwQEBCAvXv3Ys6cOViyZEm+Y8SWsGwh3nqRjMIcOSIX0ABk7+CWLUv0HK7MnGXGsavHkCPkiHi4XzjOZ55Ho9BGCDAEaByd81y44Ie4uOqW7U6dLqNevbQyHZM/M+2H59K+rM9nTExMMUcMbDksEU5ISBAxMTEOObYnSkhIAM+nffBc2o89z+XRo0CbNrI8AgCCgoAXXwRee80uh7ebrKws9O3bFz169MCkSZOK3L9u3bo4ePAgQkNDi9w3ISEBkydPxsGDB0se2LlzsnlsXuuN3r2B9etLfhwXtO/sPnT9X1ekZqYCABQo+LDRh+h+X3c0reJZq+rt3Als3apuP/ecbKFWFvyZaT88l/Z12/ksVSLM0ggi0oVmzYD//letF05LA955B9i2Tdu4rAkhMG7cODRp0qTQJPjChQvIG2DYv38/cnNzUblyZccHt2sX4OMjr/v7e8xCGjtP78R9i++zJMFeihcqBVRCkypNPC4JBmwXFQwJAcqX1y4WIlfArhFEpBsjRgA//AAsXap2khg0SJZNhIdrHR2wa9cu/O9//0Pz5s3R8lbZwdtvv43Tp08DAB5//HGsXLkSc+fOhcFgQEBAAJYvX178Gt+yiI+XyysDMiH2gPrgbX9vQ//l/WHKkl8jeCleCA0Mxd5xe/HPkX80js75hLBNhGvVkmVGRFQ4JsJEpCuffALs3Qv8/rtsgJCaCvTpAxw4APj6ahtbx44dUVQ52VNPPYWnnnrKSRFZsR46z8gAIiOdH4MTxR2PwwPfPABztpwc6K14o1pQNewZvwe1y9fGP/C8RPjqVbW0CJBtpInozlgaQUS64usLbNgga4QBmQwfPw48/bS2cemayWS7RnXz5rb9hN3M2j/W2iTBBsWAmiE1ceDRA6hd3nOzP+vRYECOCBPRnTERJiLdqVULWLkSCLg12d9sBpYsAb76Stu4dOvAAfVkeXkB3btrG48DrfhtBYatGmZJgn28fFC7Qm0cePQAaoTU0Dg6bd2q0AEgq2PCwrSLhchVMBEmIl3q1k12jbBebGPCBOC337SNS5d+/FH9Tjw4GOjsngtHLDmyBKNXj7Ykwb7evoioGIH94/ejalBVjaPTnvWIcM2asoMeEd0ZE2Ei0q3XXpMt1fJqg00moGdPdU4Y3bJpk9o/2GwG2rfXNh4HmH9oPh5d96glCfbz9kPDyg2xd/xeVA50QlcOnTOZgCtX1G2WRRAVDxNhItItLy/g22+BihXV2y5dAh56SM6QJ8jVSA4dUrdr1HC7nlmf7v8Uz2x8xpIE+3v7o1nVZtg9djcq+JexSa6bYH0wUekwESYiXatYUU6eyyuBzciQncJmzdI2Lt344w/bHln33qtdLA4wa/csTN4yWU2CDf6IDIvEjjE7EOIXonF0+nHjhm0pBBNhouJx32nFROQ2WrUCPv4YeP55+RWwySTLJtq1Azp21Do6je3apQ6PBwcDXbtqG48dzdgxA2/vfNuSBAcYAtC6RmtsGrEJAT6es2xycbRpA/zrX3KBwcuX1T8ciejOOCJMRC7h0UeB+++37STRvz9w8aK2cWlu82Z1olxurlsspCGEwKvbX8XbO9+2LJYRYAjAPbXuwZaRW5gEF8LHB6hTB2jdWutIiFwHE2EichkLFsgV5rxu/eRKSQH69VPniXmknTvV6wYDcNdd2sViB0IITNkyBR/t/cgmCe5yVxdseHgD/Ax+GkdIRO6EiTARuYyAACAuTm2plp0NHD0KTJmibVyauXQJuH5d3W7TxqXX1BVC4KkNT2HuwbmWJDjQJxC96vfCd8O+g4+3j8YREpG7YSJMRC4lIgJYulQtkTCZgHnzgNWrtY1LE7t3A363Rkj9/GRvOReVK3Ixbu04fHnkS5sk+P5G9+ObId/A4MUpLURkf0yEicjl9O8PTJxou9jGqFHAiRPaxlVSRqMRiqJYLrGxsUhMTLS5TVEUGI3Ggg+QkKA2Vfb1ddn64JzcHIxcPRJfH/3aJgke2mwoljywBN5eXBmiMEIAq1bJNVVOnQKysrSOiMi1MBEmIpf0zjtAixZyghAApKXJAdG8eWOuwGg0QghhucTHxyMqKsrmNiFE4Ynw1q1qx4iMDNlew8Vk52Zj6Mqh+O6P72yS4DGRY7Cg/wJ4Kfw1dSfXrwO//AJs2wZ8+SWwf7/WERG5Fv6EISKX5O0NrF0LlCsnt4UAkpKAMWM8ZLGN9HTgzz/V7caN1SX4XERWThYGLB+ADcc32CTBT7R+AnN6z4HiwvXOzsKFNIjKhokwEbmsKlWAdevUeuH0dGD9euCzz7SNyykOHVJfuKK4XP/gjOwM9PmqD7af3G7pExzoE4jn2z2P97u9zyS4mKwTYW9vubAgERUfE2Eicmnt2gFvv21bLzx5MnDwoLZxOdzOnTLzB4CQECAmRtNwSsKcZUb3Jd2x8/ROmyT45Y4v460ubzEJLoHTp9XrNWrIDnpEVHxMhInI5T37LNCtm9pAwWQC+vQBrl7VNi6HiosDMjPl9fR0oEMHbeMpprTMNHRZ3AX7k/bbJMFvxLyBVzu/qnF0riU9Xa4il4dlEUQlx0SYiFyeogBLlgBhYWob3evXgYED5WJrbkcI2yHvKlWAypW1i6eYbmbcROcvO+Pw+cNIz5aj2QGGALzX9T280OEFjaNzPWfP2tbD166tXSxEroqJMBG5heBg28U2srKAxERg2jRt43KIEyeAnBx1u1Mn7WIppuT0ZNyz8B4cvXQUGTkZAGQSPLvXbExsM1Hj6FyTdVkEwBFhotJgIkxEbqNxY7kMs3W98EcfARs3ahuX3e3apa4zHRQk60J07KrpKtrNb4c/r/5pkwTP6zsP41uN1zg612U9Ua5SJflWIKKSYSJMRG5l6FDZQi2voYLZLG/75x9Nw7KvbduA1FR1W8cLaVxKu4Q289vg7+t/IzNH1jQHGALw5YAvMSJyhMbRua7cXNkuMA/LIohKh4kwEbmdjz8GGjVSZ9CnpQG9esk1J9xCQoLtdsOGmoRRlHMp5xA9Lxqnb5xGVq5c8izAEIDlg5bjwWYPahyda7twQZ0rCbAsgqi0mAgTkdvx8ZH9hIOD5XZurlx+9vHHNQ3LPq5dAy5dUrdbt1ZnCOrImRtnED0vGkkpScjOzQYgu0N8++C36N+4v8bRub7bF9LgiDBR6TARJiK3VKMGsHq1bYnEN9/IZWhd2p49gL+/vO7jA/TooW08BTh5/SRaf94aF9MuIkfISX1BPkH4ftj36Nmgp8bRuQfrv4X8/YHQUO1iIXJlbL1NRG4rJgaYOlUuuGEyycvEiUCrVkCLFlpHV0o//KDWBwcEAB07ahvPbY5fPY72C9rjevp15ArZuy7IJwhxI+LQsba+YnVlffvKZiFnzsh+wjr8UoDIJXBEmIjc2iuvyFzRerGNXr2AGze0javUtmxRmyObzbI0Qid+u/wb2s5vi2vma5YkONg3GNtHb2cSbGeKAlSoADRvDkRHax0NketiIkxEbk1RZEmE9XoTV68CDz5ouxiBS8jKAn77Td2uX1+t/dDYzxd/RocFHXA9/ToE5Ikt51cOP4z5AW1qttE4OiKigjERJiK3V7687CWc1184I0O24p05U9u4jEYjFEWxXGJjY5GYmGhzm6IoMBqN8gE//aQObSsKcN99msVuLfFcIjou7IgbGeowewW/Ctj5yE60qt5Kw8iIiO6MiTAReYQWLYBPPlGT4bQ04K238ncicyaj0QghhOUSHx+PqKgom9uEEGoivHOn2jMrJASIjdUs9jx7zuxBzKIYpGSmAAAUKKgUUAl7xu9B82rNNY6OiOjOmAgTkccYM0aWRFh3khg4EDh3TtOwim/TJrUZckYG0KGDpuHs+GcHuv2vG1Iz5eQ9L8ULlQMrY9/4fWgc2ljT2NxVZiawbh1w5Ahw/boLlvcQ6QwTYSLyKJ99BtStq65QnJoqZ+BnZWkaVtGEAPbtU7fLlwfCwjQLZ8tfW9BraS+kZaUBALwVb1QNrIoDEw6gfqX6msXl7s6eBQ4elK0B//Mf4I8/tI6IyLUxESYij+LnJ+uF8xbbyM4Gjh0Dnn9e27iK9M8/tkvjadg2bf2f6zHg6wEwZZkAAAYvA8KCw3Dg0QOoW6GuZnF5gtsX0qhZU5s4iNwFE2Ei8jh16gDLl6slEiYT8MUXsruEbu3apa4ZHRgIdOumSRjf/fEdhqwYYpME1wypiQMTDiC8XLgmMXkS60S4QgWgXDntYiFyB0yEicgj9eolR4HzJs+ZTMDYsTr+qnn7diBFTkiDl5cmI8LLf12O4auGw5xtBgD4ePmgboW6ODDhAKqHVHd6PJ4mN9c2Ea5VS7tYiNwFE2Ei8lhvvglERcmVigGZDPfsqS7cpivx8er17GygaVOnPv3inxZj7JqxliTY19sX9SvVx77x+1AlqIpTY/FUly/bVsfUrq1dLETugokwEXksLy856ahCBbktBHDxIjBihM5m49+8KWdJ5fnXv9TZfk4wL3EeHl//uCUJ9vP2Q+PQxtgzbg8qBVRyWhye7vb6YI4IE5UdE2Ei8miVKwPr16v1wunpwNatcka+buzbpwZoMAA9ejjtqWfvm43n4p6zJMH+Bn80r9YcOx/ZifL+5Z0WBwGnT6vX/fyAqlW1i4XIXTARJiKPFx0NfPCB7WIbr7wC7NmjbVwWO3bIoAAZZKdOTnna93e9j39v/bclCQ4wBKBV9Vb4YcwPCPELcUoMpLIeEQ4Pd+qXAkRuix8jIiIATzwB9OkD+PvLbbMZ6NdP1mVqbtMmICdHXjebgbZtHf6Ur//wOow/GG2S4LY122LbqG0I9Al0+POTrZQUuYBGHpZFENkHE2EiIgCKAnz5JVCjhrwOyNLc/v3VHFQTOTnAzz+r23XqAEFBDns6IQRe3voy3tv1nqVFWqBPIDrX6YxNIzfB3+DvsOemwrE+mMgxmAgTEd0SGAjExaklEllZMgf99781DOqXXwBfX3W7SxeHPZUQAs9veh6z98+2SYLvu+s+fP/Q9/D19i3iCOQo1omwosjSCCIqOybCRERWGjQA/vc/28U2Pv0U+P57jQLauVO2SwOAkBCHJcJCCDy+/nF8fuhzmyS4T4M+WD10NXy8fRzyvFQ8SUnq9WrV5GQ5Iio7g9YBEBHpzcCBwKOPAp9/LhNhkwkYPhw4cgSIiHByMJs3y7pgQA5R33OP3Z8iV+Ri7JqxWPHbCpsk+IHGD2DRwEXwUjhmorWRI4Fz5+TIsD+rU4jshj/diIgK8MEHcs2KvFWNTSa5Gl1eTuo01q0rAgPt/p14Tm4Ohq8ani8JHt58OJNgHfHxkeXhHTsCrVtrHQ2R++BPOCKiAhgMshwi5FaXsLzlbcePt99zGI1GKIpiucTGxiIxMdHmNuXKFRjzHtC+vf2eHEB2bjYGfTMI3x/73iYJHttyLOb1ncckmIjcHn/KEREVIixMJsN59cJmM/Ddd8C8efY5vtFohBDCcomPj0dUVJR629dfQ4SEyETY39+uC2lk5mSi/7L+2PzXZpiy1SR4YvREzO41G0pe6wwiIjfGRJiI6A7uuQd44w21k4TJBDz3HHD4sBOePD5eNpAF5HfjdqoPTs9OR68lvZBwKsHSJzjQJxCT20/Ge93eYxJMRB6DiTARURFeeAGIjVVn6pvNQO/etgscOMS2ber1zEygRYsyH9KUZUK3xd2w5+wemyT41c6v4vXY18t8fLKv5GS5sOCpU3KuJBHZF7tGEBEVQVGAZcvk5LmzZ+Vt164BgwYBW7c6aKnbtDSZ/eRp3lyduVdKqZmpuG/Rffj54s9Iz0kHAAQaAjGjyww81+65Mh0cmqUqAAAgAElEQVSbHOPvv4Ht2+V1Ly/g8ceBqlW1jYnInXBEmIioGEJC5ErHeSUSmZnAvn2ybMIhDhxQi5O9vYHu3ct0uJsZN9Hpi044cvGIJQkOMATgg+4fMAnWMeuFNLy9gcqVtYuFyB0xESYiKqamTeVEOet64ffek61+7e7HH+UTAHJJ5c6dS32o6+br6LCgA36//DsycjIAyCT4k96f4InoJ+wRLTnI6dPq9Zo1ZTJMRPbDRJiIqAQeflherDtJPPig7cidXWzapK4oZzYD7dqV6jBXTFfQdn5bHL923CYJnt9/Ph751yP2ipYcIC0NuHpV3a5VS7tYiNwVE2EiohKaMweoX18dnUtNlZPnMjPt9AS5ucChQ+p2zZpA+fIlPszF1IuI/jwap5JPITNHBhdgCMCSB5ZgePPhdgqWHCWvHj1P7draxEHkzpgIExGVkK8vsGEDEBwst3NygL/+AiZOtNMT/P677Xfg995b4kMk3UxC689b4+zNs8jKle0GAgwB+GbwN3igyQN2CpQcybosArD7ooJEBCbCRESlEh4OrFxpWyLx1VfAkiV2OPiuXXJUGJDZdteuJXr4P8n/IPrzaJxPOY/sXFleEWgIxOqhq9G3UV87BEjOYF1uU6WK+l4jIvthIkxEVEpduwIvvWQ7ee6xx4CjR8t44C1b1IlyOTklWkjjr2t/IfrzaFxMu4gckQNA9gle//B69Khvv5XpyLGys4Fz59RtlkUQOQYTYSKiMpg2DWjbVpZLADJ/7dkTuHmzDAfduVO97usL1K1brIcdu3IMbea3wRXTFeQKOaIc5BOELSO3IKZuTBkCImc7f16dKwlwohyRozARJiIqAy8vYNUqoFIl9bbLl4GHHgKEKMUBs7Jsl6xr21au6FGEo5eOot2Cdrhuvg4B+cQhviFIGJOADrU6lCIQ0tLtXUiYCBM5BhNhIqIyqlhRTp7Lq+HMyAB++AH44INSHCwtTV3L2c8P6FF0OcNPF35Ch4UdkJyebEmCy/mVw45HdqB1jdalCIK0Zj1RLijI9g8tIrIfJsJERHbwr38Bs2er9cJpacD06XJdjBJJSZEXQCbCRdQHH0g6gM5fdMbNDFmLoUBBBf8K2D12N1qGtSzhk5MeCGE7IlyrVrG+FCCiUmAiTERkJ+PHAwMG2HaSuP9+4MKFgvc3Go1QFMVyiY2NReKlS1CEgAJAuXkTSrt2MBqNBT5+95ndiF0Ui5RMmTgrUFApoBL2jd+HZlWb2f8FktNMmAAMGgRERwNNmmgdDZH7YiJMRGRHCxbIGf5et366pqQA/frZTnzKYzQaIYSwXOK3b0eUokAA8hIZCSFEgYlwwqkEdP9fd6RlpQEAvBQvVAmqgv0T9qNh5YYOe33keIoCVKgANG8O9OkDREZqHRGR+2IiTERkR/7+wMaNsq4TkAnwb78BkycX48Emk/oduKIA3boVuNumE5vQZ2kfSxLsrXijWlA17B+/HxEVI+zwKoiIPAMTYSIiO7vrLrm4Rl6JhMkEfP458O23RTwwJUVtNRESUuCKct8f+x4Dvx4IU7bsM2zwMqB6SHUcmHAAdSrUseOrICJyf0yEiYgcoG9f4OmnbRfbGDUK+PPPOzzo5k01EU5PBzrYtj1b+dtKDF05FOZsMwDAx8sHtcrVwsEJB1GzXE0HvAoiIvfGRJiIyEHeflvWd/r4yO28xTbS0grYWQjbO6pUsemZ9dUvX2HU6lGWJNjX2xd1K9TF/gn7US24mgNfBTnTxYvAkSPAtWul7ENNRCXCRJiIyEG8vYE1a4By5eS2EHLFsNGjC0hyjh+33e7c2XL1i8NfYPza8ZYk2M/bD/Ur1ce+8fsQGhjqwFdAznb0KLB6tWzFN2sWkJmpdURE7o2JMBGRA1WpAqxbp9YLp6fLyXSffnrbjrt2qdeDgiwT5eYemIuJGybaJMFNqjTBnnF7UDGgohNeATmT9UIafn7q0t1E5BhMhImIHKxdO+Cdd2zrhadMAfbvt9pp61YgN1deFwK45x58tPcjvLD5BUsS7G/wR2S1SPz4yI8o51fOuS+CHC4nB0hKUre5rDKR4zERJiJygqefBrp3l+3VALnYRt++wJUrt3bYsUPd2csLMy+uwqvbX7UkwQGGALSu0RoJYxIQ7Bvs3ODJKS5eBLKy1G0mwkSOpwgHVOMriiIAwBHH9kTKrb6iPJ9lx3NpPzyXJZeWBtx9N/DPP3LQ19dXrhz2w+prMFStDACIAtBnTB180OAyTFmyRVqAIQAdanXAuuHr4G/w1/AVuAZXfW/u3QvExanbEyfK0hotueq51COeS/sq4HyWaiFyXY8IF7asqDOPoYcY7EEvr0MP/x/2oIfXoZdj6CEGV/n/CAqSiU5eiURmJnD4MDBt4jXLPmfLAR/UPWdJggMNgYipG4MND28oMgnWw7m0xzH08L4EnP86zpxRrwcEAKGhPJf2eryejqGHGNzl/8MedD0irCiK5sfQSwxA2c6nHl6HPY6hh3Nprzi0jqGsx9DLubTHMUr6+Li4ODz77LPIycnB+PHj8e9//9vmGBkZGRg1ahQSExNRuXJlfP3116hbt67l8StWyM4RZln1gABDJszZfgAArzAg93F5e6BPIHrU64FvhnwDg5fB7q9Dr8fwxM+5EMBHH8lW0gDQoAHw8MM8l/Z6vB6OoZdzaY9j6CUGwM1HhImI9CYnJwcTJ07Exo0b8dtvv2HZsmX47bffbPZZsGABKlasiBMnTuD555/HSy+9ZHP/kCHA2LHqyLA5R01yc2/9KA/0CUS/hv2wYsiKYiXB5Npu3FCTYACoXVu7WIg8CRNhIqIS2L9/P+rXr4+IiAj4+vpi2LBhWLNmjc0+a9aswejRowEAgwcPxrZt2/KNfHz0EdCoEWAwCKDH8zb3BfoEYkjTIfhq0Ffw9vJ27AsiXbAuiwA4UY7IWZgIExGVQFJSEmpZZSnh4eFIsu55dds+BoMB5cuXx9WrV2328fVVcPiwguxsLyButnrHecA01YRFAxfB28sbiqJYvgIk92WdCHt5ATW5YjaRUzisRrhevXrw9i7bSIbJZEJg3neHGh1DLzEAcPnXYY9j6OFc2isOrWMo6zH0ci7tcYySPD4lJQVpaWkICwsDANy8eRPp6ekIDg62HOPUqVMIDw+HwSBLGk6ePInatWvb/Ez8888/SxRjw4YN7fo69HwMT/ycJyf7ICdHjk0ZDLkoXz7L6TEU9njAtc6lXo+hl3Npj2PoJQZAPZ9//vnnJiFEz5Ieh5PlXCQGgJPl7PV4QPv3ph7OZVmPoZdzaY9jlOTxe/bsgdFoxKZNmwAAM2fOBAC88sorlmP06NEDRqMR7du3R3Z2NsLCwnD58uVCR3bffhuYOjXvvigEBh7E7t1AZKTjXoeej+Fpn/OMDLngSt6u7doBPXs6N4Y7PR5wnXOp52Po5Vza4xh6iQHgZDkiIqeKjo7G8ePHcfLkSWRmZmL58uXo37+/zT79+/fHokWLAAArV65Ely5d7lje8PLLttsmE9CrF5CcbPfwSYcMBuCRR4CuXWXdeESE1hEReQ5ORSYiKgGDwYA5c+agR48eyMnJwdixY9GsWTMAwNq1a9G/f3+MGzcOI0eORP369VGpUiUsX778jscsKEe+dk12l9i0SdaMkvvy9pZdItgpgsj5WBrhIjEALI2w1+MB7d+bejiXZT2GXs6lPY6hlxgAwMsrCrm5BwHI9movvwy8+qpzYtDLMfg5108MPJf2O4ZezqU9jqGXGAA3L42YPn265sfQQwz2oJfXoYf/D3vQw+vQyzH0EIO7/H8AclQwb/6IySTrh+PjnReDHo6hh/cloI/XoYcY7EEPr0Mvx9BDDO7y/2EPDhkRBoCEhAQRExPjkGN7ooSEBPB82gfPpf3wXNpXQkICJk+ejBYtDmL5cnXlufLlgaNH2VKrJPjetB+eS/vhubSv286n+40IExF5orlzgbvukrWjAJCWBvTpA2RlaRsX2d+5c8CpU/y/JdIKE2EiIp3x8wM2bgSCguR2djZw/DjwzDPaxkX2t3cv8OWXwMyZwOLFWkdD5HmYCBMR6VDt2sDXXwMBAXLbZJKJUhENKMjFnD4t/83NLbh7CBE5VpkSYUVRhiiKclRRlFxFUVpb37d06VLUr18fjRo1sjSev93JkyfRtm1bNGjQAEOHDkVmZmZZwnErQ4cORcuWLdGyZUvUrVsX48ePL3C/unXronnz5mjZsiVat25d4D6ezmg0ombNmpbzuXfv3gL3i4uLQ6NGjVC/fn288847To7SNUyZMgWNGzdGixYtMHDgQKSmpha4H9+XhSvqfSaEwNChQ1G/fn1Mn94W48adspk8N24c8PvvTg5ap86cOYPY2Fg0adIEzZo1w3/+8598+yQkJKB8+fKWz/8bb7yhQaQFS0mx7RWtdfu0oj63Qgg888wzqF+/Plq0aIFDhw5pEKX+HTt2zPJ+a9myJcqVK4ePP/7YZh89vy/1YOzYsahatSruvvtuy23Xrl1Dt27d0KBBA3Tr1g3Xr18v8LGKooxWFOX4rcvoIp9MCFHqC4AmABoBSADQ2ur2phERESI9PV38/fffIiIiQmRnZ4vbDRkyRCxbtkwIIcRjjz0mPv3003z7kBCTJk0SY8aMKfC+OnXqiMuXLzs5Itcyffp08f7771u24+Pj8+2TnZ0tIiIixF9//SUyMjJEixYtxNGjR50YpWvYtGmTyMrKEkII8eKLL4phw4YVuB/flwUr6n0WHx8vateuLR577DEhhBDLli0TQ4Y8KDp3FsLXVwhACEURonZtIVJStHoV+nHu3DmRmJgohBDi5s2bokGDBpbzmfc5j4+PF3369NEqxDs6elSI6dPVy19/aRtPYZ/bvHO5fv160bNnT5Gbmyv27Nkj2rRp4+QIXU92draoVq2aOHXqlBDCNd6XevDDDz+IxMRE0axZM8ttU6ZMETNnzhRCCDFz5kzx4osv3v77HAAqAfj71r8Vb12vKO6Qy5ZpRFgI8bsQ4lgBd93fpUsX+Pn54a677kL9+vWxf//+fAn49u3bMXjwYADA6NGj8d1335UlHLckhMA333yD++67T+tQ3Nr+/ftRv359REREwNfXF8OGDcOaNWu0Dkt3unfvDoNBrsPTrl07XL58WeOIXEtx3mfJyckYPVoOYgwePBjbt2/DqlUCFSrI+4UALl0CHn5YXZLXU1WvXh2tWrUCAISEhKBJkyZISkrSOKriyyuLAGRZhN67gqxZswajRo2Coiho164dkpOTcf78ea3D0rVt27ahXr16qFOnjtahuJTOnTujUqVKNretWbPG8rPxDjljDwBbhBDXhBDXAWwB0PNOz+WoGuGaVatWtWyEh4fn++F09epVVKhQwfJLtaB9CPjxxx9RrVo1hIeHF3i/oijo3r07oqKiMG/ePCdH5zrmzJmDFi1aYOzYsUhJScl3f1JSEmrVqmXZ5vuxaAsXLkTbtm0LvI/vy4IV532WmZlp2cdgMKB8+fIArmL9erVeOD0d2LoVuO3bVo926tQpHD58uMD35J49exAZGYlevXrh6NGjGkRXsDNn1OthYXKSpJaK+tzy52TJLV++HA899FCB9+n1falXFy9eRPXq1QHIP4IvXbpU0G41AVh9snD21m2FKnKJZUVRtgIIK+CuqUKIwobM8pX8K7fNAhAFDGXcvo+769q1Ky5cuJDv9hkzZuD+++8HACxbtqzQDxEA7Nq1CzVq1MClS5fQrVs3NG7cGJ07d3ZYzHp1p3P5xBNPYNq0aVAUBdOmTcOnn36Kfv362ezH96OqOO/LGTNmwGAwoGvXrgUeg+/LgpX2faYoClq3BmbNAiZPlrXCJhMwdSrQrh3Qvr0jonUdqampGDRoED7++GOUK1fO5r5WrVrhn3/+QXBwMDZs2IABAwbg+PHjGkWqysoCrAdTrfJLzRT1ueXPyZLJzMzE2rVrMXPmzHz36fV96QYKekPe8buzIhNhIUTBv+nu7Kx1pn727FnUqFHDZofQ0FAkJycjOzsbBoOhwH3c3datW+94f3Z2Nr799lskJibixIkTBe6Td86qVq2KgQMHYv/+/R6ZcBR1LvNMmDABsbGx+W4PDw/HGavhGU98P+Yp6lwuWrQI69atw7Zt2/KVPOXh+7JgxXmf+fr64syZMwgPD0d2djZu3Lhh+Yrw8ceBH34A1qyRo8JmM9C3r5w8Z/UlnEfJysrCoEGD8PDDD+OBBx7Id791Yty7d288+eSTuHLlCkJDQ50ZZj5JSbJTRB49JMJFfW75c7JkNm7ciFatWqFatWr57tPr+1LPqlWrhvPnz6N69eo4f/48qhb8Q+8sgBir7XDIeWyFclRpxNrt27cjIyMDJ0+exPHjx9GmTRubHRRFQWxsLFauXAlA/nLNG20iaevWrWjcuHGhZRFpaWmWr/nT0tKwefNmmxmWJFnXsK1evRp33XVXvn2io6Nx/PhxnDx5EpmZmVi+fDn69+/vzDBdQlxcHN59912sXbsWgXmtDG7D92Xhbn+fffzxx3jllVegKIrlZ+LNmzfRoUMHKIoCHx8fXL16Fa+//joAWUe6cCEQHq622kpJAfr3l72GPY0QAuPGjUOTJk0wadKkAve5cOGCZSRz//79yM3NReXKlZ0ZZoGsyyIA7TtGFOdz279/fyxevBhCCOzduxfly5e3fFVN+d3pG129vi/1rH///li0aBGAO+aMmwB0VxSloqIoFQF0v3Vb4e40k66oC4CBkNl3BoCLADbl3Tdu3DgREREhGjZsKDZs2GCZ0terVy+RlJQkhBDir7/+EtHR0aJevXpi8ODBIj09vQxzDN3P6NGjxdy5c4UQ6kzTpKQk0atXLyGEPH8tWrQQLVq0EE2bNhVvvfWWVqHq2ogRI8Tdd98tmjdvLvr16ydWrlwphLA9l0LIGdENGjQQERERPJeFqFevnggPDxeRkZEiMjJS9OvXTwjB92VJFPQ+mzZtmlizZo2Ij48XrVq1EoMHDxb16tUT0dHR4q8CWgkcPy5EcLDsIgEIERgoxAsvOPuVaO/HH38UAETz5s0t78n169eLuXPniueff14IIcT//d//iaZNm4oWLVqItm3bil27dmkctbR0qdotYtYsIXJztY2nsM+t9bnMzc0VTz75pIiIiBB33323OHDggJYh61paWpqoVKmSSE5OttzmCu9LvRg2bJgICwsTBoNB1KxZU8yfP19cuXJFdOnSRdSvX1906dJFXL16VcTHx4sDBw6IcePGCaHmpmMBnLh1eUQUkcsqwkHTjhMSEgTX07Yfrk9uPzyX9sNzaV8JCQmYPHkyDh48WOS+330HDB8uyyMAOZFu2TKAX6xJen5vCgG89576f9esGTBkiLYx3Ymez6Wr4bm0r9vOZ6kK1rmyHBGRCxowQNYM51WomM3AiBHAX39pGxcV7coVNQkG9FEfTOSpmAgTEbmo994D7r4buNWFEiYT0LOnbZJF+hMSAgwaBLRpI9umaV0fTOTJiuwaQURE+mQwAGvXAk2bAteuyS4ESUnAI4/IMgl2ttInf3+geXN5ISJtcUSYiMiFVasmk+G8xTbMZuD77wGuY0JEVDQmwkRELu6ee4A331TrhU0m4PnngcREbeMiItI7JsJERG5g0iSgSxd1mV6zGejdW5ZMEBFRwZgIExG5AUUBvvrKdoW55GTggQdsVzAjbZ0/L/84cVDnUiIqISbCRERuIiQEiItTSyQyM4EDB4BbC9ORDmzcCMyeDcyaBWzerHU0RMREmIjIjTRtCnz+uW298PvvM+nSg+xs4Nw5eT01FcjI0DYeImIiTETkdoYPl4trWHeSGDIEOH1a27g83fnzMhnOw/7BRNpjIkxE5Ib+7/+ABg0Ab2+5nZYmJ89xFFI7Z87YbnNFOSLtMREmInJDvr7Ahg1AcLDczskB/v4bePJJbePyZNYj8kFBQMWK2sVCRBITYSIiN1WzJvDtt7YlEsuXA4sXaxuXJxLCdkS4dm2u/EekB0yEiYg0YjQaoSiK5RIbG4vExESb2xRFgdFoLPVzdOkCvPyy7eS5J54AfvnFPq+Biuf6dVmekodlEUT6wESYiEgjRqMRQgjLJT4+HlFRUTa3CSHKlAgDwNSpQIcOslwCkMlwr17AzZtlfw1UPLdPVGQiTKQPTISJiNyclxewYgVQubJ625UrwNChXNjBWazLIgwGoHp17WIhIhUTYSIiD1Chgpw8l1cikZEB7NgBvPeetnF5CusR4Ro1ZDJMRNpjIkxE5CFatpRt1azrhV9/XSbE5DhmM3D5srrNsggi/WAiTETkQcaOBQYNsu0kcf/9crEHcoyzZ223uZAGkX4wESYi8jDz5slkzOvWb4DUVKBvXyArS9u43FVoKNC1K9CokRyNDw/XOiIiysMqJSIiD+PvD2zcCERGAikpctnfP/4AXngBmD1b6+jcT8WKQMeO8roQ7B9MpCccESYi8kB33QUsW6aWSJhMwPz5wKpV2sbl7pgEE+kLE2EiIg/Vpw/wzDPq5DmzGRg9GvjzT23jIiJyFibCREQebMYM2U3Cx0dum0xAz562q6AREbkrJsJERB7M2xtYswYoV05uCyE7SIwaxcU27OHyZSAzU+soiKgwTISJiDxcaCiwfr1aL5yeDsTFAXPmaBuXqxMCWLwYeOcd2anj0CGtIyKi2zERJiIitG0rV5mzXmzjpZeAffu0jcuV3bghu3Lk5gLnzslzSkT6wkSYiIgAABMnyvpgf3+5bTbLCXXWq6JR8Z05Y7vNFeWI9IeJMBERAZCtvRYvBqpXV9t83bwJDBgA5ORoG5srOn1ave7tDdSooV0sRFQwJsJERBoxGo1QFMVyiY2NRWJios1tiqLAaDQ6LaagIFkfnFcikZUF/PQTMHWq00JwG9YjwtWrq505iEg/mAgTEWnEaDRCCGG5xMfHIyoqyuY2IYRTE2EAaNgQWLTIdrGN2bOBdeucGoZLy8gALl5Ut1kWQaRPTISJiCifQYOA8eNtF9sYPhw4eVLbuFzF2bO27eeYCBPpExNhIiIq0IcfAk2aAAaD3E5LA3r1ku3V6M5unyhXu7Y2cRDRnTERJiKiAhkMwPffAyEhcjs3V04Ae/RRbeNyBdaJcMWKQHCwdrEQUeGYCBMRUaGqVwe++06tFzabgVWrgAULtI1Lz3JzZWlEHpZFEOkXE2EiIrqjzp2B6dNtF9t45hnZTYLyu3RJTpbLw7IIIv1iIkxEREV68UWZEPv5yW2TSdYLJydrG5cecSENItfBRJiIiIqkKMDXXwOhoept164BgwfLUgBShYUB0dHy34AAoEoVrSMiosIYtA6AiIhcQ7lycrGNtm3liHBmJrBnDzBjBjBtmtbR6UetWuoocHY24MUhJyLd4seTiIiK7e67gc8+s60XnjkT2LZN27j0ysDhJiJdYyJMREQlMnIkMGyYbSeJQYNsOyUQEbkCJsJERFRin34K1KsHeHvL7dRUoE8fWS5BROQqmAgTEVGJ+fkBGzYAQUFyOycHOH4cePppbePS2s2btksrE5G+MREmIqJSqVULWLHCtkRiyRLgq6+0jUsrWVnAxx8Ds2bJDhsnT2odEREVhYkwERGVWvfuwJQptpPnJkwAfvtN27i0kJQkW8mlpgK//w6kpWkdEREVhYkwEZFGjEYjFEWxXGJjY5GYmGhzm6IoMBqNWod6R9Ony765vr5y22QCevYEUlK0jcvZuJAGkethIkxEpBGj0QghhOUSHx+PqKgom9uEELpPhL28gG+/BSpWVG+7dAkYPtyz6mVPn1avlysHlC+vXSxEVDxMhImIqMwqVQLWr1frhTMygO3bgQ8/1DYuZxHCdkS4dm3tYiGi4mMiTEREdhEVBXz0kW298LRpwK5d2sblDFeuAOnp6jbLIohcAxNhIiKym0cfBfr3B/z95bbZDPTrB1y8qG1cjmZdFgEwESZyFUyEiYjIbhQFWLgQCA+XtcOAnDTXvz+Qna1tbI5kXRbh6wuEhWkXCxEVHxNhIiKyq4AAIC5OLZHIzgZ+/RV48UVt43Ik6xHhmjXVPwKISN/4USUiIrurV08urpE3ec5kAj77DPjuO23jcoS0NODaNXWbZRFEroOJMBEROcT99wNPPqmODJvNwMiRwIkT2sZlb7f3D2bHCCLXwUSYiIgc5p13gObNAR8fuZ2WJhfbMJm0jcuerMsiFEXWRxORa2AiTEREDmMwAGvXAiEhclsIuRTxmDHus9hG9epAo0Zy5LtqVbVjBhHpn0HrAIiIyL1VrQqsWwfcd58sj0hPl4tvfPYZ8MQTWkdXds2by4sQ7jXSTeQJOCJMREQO1749MGOG7WIbL7wAHDyobVz2pChAUJDWURBRSTARJiIqhilTpqBx48Zo0aIFBg4ciOTk5AL3q1u3Lpo3b46WLVuidevWTo5S3557Duja1Xaxjd69gatXtY2LiDwXE2EiomLo1q0bfv31V/z8889o2LAhZs6cWei+8fHx+Omnn3DQnYY77UBRgKVLZamEosjbkpOBgQOB3FxtYyMiz8REmIioGLp37w6DQU6raNeuHc6ePatxRK4pOBjYtEntL5yVBSQmAq+9pm1cpSGEjJ+IXBcnyxERldDChQsxdOjQAu9TFAXdu3eHoih47LHH8Oijjxa6X2EKuk+4S4sFAI0bAwsWAOPGyVphkwn48EOgY0fZWs1VXLsGfPKJXE65dm2gdWsgNFTrqIioJBRH/XBdv369COKsAbtJTU1FcHCw1mG4BZ5L+3G3c/nCCy/gmvUSYbeMGzcOHTt2BAAsWbIEx44dwxtvvFFgwnrlyhWEhobi+vXrmDx5Mp555hlERkbm2y82NrZEscXHx5dof1dw+rSsD84ri/D2Bpo2BXx9y35sZ7w3T5wIxs6daubbp895VKmS4TvypUoAABibSURBVNDn1IK7fc61xHNpX9bnMyYmpvDRhTtw2IhwUFAQYmJiHHV4j5OQkMDzaSc8l/bjbucyMTHxjvcvWrQIR48exbZt2xCY1/7gDo4cOYKsrKwCz1FBgxAJCQmYPHmyx9QWZ2UBbdoAv/4KZGfLRLhRI+DQIcDPr2zHdsZ7MyUFqFtXXjcYgAceqAtvb4c+pSbc7XOuJZ5L+7LH+WSNMBFRMcTFxeHdd9/F2rVrC02C09LSkJKSYrm+efNm3H333c4M06X4+Mj+wnlfHubkACdPuk5vYesV5WrWhFsmwUTujokwEVExPPXUU0hJSUG3bt3QsmVLPP744wCAc+fOoXfv3gCAixcvomPHjoiMjESbNm3Qp08f9HSlolcN1KwJrF6tTp4zm4GvvwYWLdI2rqKYzcDly+p2rVraxUJEpcfJckRExXDixIkCb69RowY2bNgAAIiIiMCRI0ecGZZbiI0FXnkFmDlTnTz35JNAq1ZyxTY9OnPGdpuJMJFr4ogwERFpbupU4J571IlyJpPsIHHjhrZxFYaJMJF7YCJMRESaUxTgm2+AypXV265eBR58UPbr1RvrRDg0VF06mohcCxNhIiLShQoVgI0b1aQyIwPYuVOWTOhJTg6QlKRuczSYyHUxESYiIt2IjATmzFGTYZMJeOstICFB07BsXLhgu6Jc7draxUJEZcNEmIiIdOWRR4DBg207SQwcCJw7p21ceVgfTOQ+mAgTEZHu/Pe/crEKr1u/pVJTgb59bUditWLdPzgw0LaumYhcCxNhIiLSHX9/YMMGdbGN7Gzg2DHg+ee1jQsAqlYFwsLkBL9ateS/ROSa2EeYiIh0qW5dubjGoEGyPMJkAr74AujcWXaT0EpMjLxkZADp6drFQURlxxFhIiLSrV69gOees508N3asHB3Wmp8fUL681lEQUVkwESYiIl178025ypyPj9w2mYAePWTdMBFRWTARJiIiXfP2Blavln2GAbnAxsWLwIgR+lxsg4hcBxNhIiKNGI1GKIpiucTGxiIxMdHmNkVRYDQatQ5Vc6GhwPr1aku19HRgyxbg//7PeTEIwcSbyN0wESYi0ojRaIQQwnKJj49HVFSUzW1CCCbCt0RHA++/b1sv/O9/A3v3Ouf5//4bmDVLTuDbvVs+PxG5NibCRETkMp58EujdW7ZXA2Q3ib59gcuXHf/cZ87IuuTffwc2bwZycx3/nETkWEyEiYjIZSgKsGgRUKOG2r/35k3g/vuBnBzHPrf1QhoVKwLBwY59PiJyPCbCRETkUgIDgbg4tUQiKws4cgR4+WXHPWduLnD2rLpdu7bjnouInIeJMBERuZwGDYDFi9XJcyYTMGcO8P33jnm+S5eAzEx1u1YtxzwPETkXE2EiInJJDzwATJigjgybzcDw4XJSm71Zl0UATISJ3AUTYSIiclmzZgFNmwIGg9w2meRqdPZuc3bmjHrd3x+oWtW+xycibTARJiIil2UwyHKIkBC5nZsrk9ZTp+z7PNaJcHi4OlGPiFwbE2EiInJpYWHA2rVqvbDZDCQnA/Pm2ef4N2/K4+VhWQSR+2AiTERELq9jR+D119V64dxc4LnngMOHy35s69FggB0jiNwJE2EiInILkycDMTGAn5/cNptlvfD162U7rnUi7OUF1KxZtuMRkX4wESYiIregKMCyZUCVKupt168DgwaVbRU4644R1aoBvr6lPxYR6QsTYSIichvlysnFNrxu/XbLzAT27QPefNN2v//+17butzBCAOXLqyUXLIsgci8GrQMgIiKyp2bNgGPHZPJqMsnLu+8CHToA3brJfebMAW7cAF588c7HUhRg6FCZEF+9Cnh7Oz5+InIejggTEZHbqVRJLq5h3UliyBB1meR77gE++ADIzi7e8RQFCA0FKlZ0TLxEpA0mwkREGjEajVAUxXKJjY1FYmKizW2KosBoNGodqkv65BOgXj11FDc1FejdW5ZLxMQAly/LtmtE5LmYCBMRacRoNEIIYbnEx8cjKirK5jYhBBPhUvL1BTZsAIKC5HZODnDiBDBxoiyTAIC33tIuPiLSHhNhIiJyW7VqAStX2pZIfPUVsGMHUKEC8NNP8kJEnomJMBERuZ2kJGDECNn6rFs3OSkur/ODyQQ89pisIxYCmDmz4GMcPixXp9u4ETh6VI4oE5F7YSJMRERup0oV4OBBWSP85JPAE08AbdqoPYBNJuDvvwEfH1knfPFi/mOcOgWcOyfbr61ZIyfMEZF7YSJMRERux9cXOHQIGDAAmDtX9v9t3FhddQ6Q1w23moh+8kn+Y1ivKFejhsC//hWJRYsWAQBWrlyJDh06oHLlyvD390ejRo3w1ltvITMz04GvqniSkpIQHBwMRVGQmppqc9/EiRMxbtw4jSIj0h8mwkRE5JYCA4FvvgE+/li2SZs3T3aO8PGR92dkyJrh9HRg9mzZTSJPaipw7Zq6/fff3+D69esYPnw4AODq1auIjY3F/PnzsXHjRowdOxYzZszApEmTnPgKCzZlyhQEBwcXet/SpUtx4sQJJ0dFpE9MhImIyG0pCvDss3JyXPnycsU5gyH/whg5OcDXX6vb1qPBALB+/WyMHDkSPrey6MceewwzZszAwIEDERsbi5deegmTJk3CkiVLIIRw8Ksq3I8//oi4uDhMnjy5wPvr1q2Ljh07Yu7cuU6OjEifmAgTEZHbu+ceOeGtRQu5ffvEt9RUYMYMOXkOsE2Er107gUOHdmPw4MF3fI7KlStrWhqRk5ODp59+Gq+99hpCQ0ML3W/QoEFYunQpcnNznRgdkT4xESYiIo9Qvbqc+DZypNpBwtrZs8Du3fK6dSJ85co2BAUFITIyMt9jcnJyYDKZsHPnTsyePRtPPPEEFI1m1X322WdIT0/HxIkT77hfhw4dcPHiRfzyyy9OioxIv5gIExGRx/DxAf77XzmB7vZkOC0NePttWU987px6+7VriWjSpAm8vPL/ygwKCkJQUBA6deqEe++9F++//76DX0HBrl69imnTpuHDDz+0lG8UplmzZvD29sb+/fudFB2Rfhm0DoCIiMjZRo0CIiOBnj3lpLi8ioZt22TbNevSifT0C4WWGuzevRsmkwn79+/HG2+8gaeeegqffvppqWK6ceMGzp8/X+R+jRs3znfb1KlT0bZtW/Tu3bvIxxsMBlSoUAEXLlwoVZxE7oSJMBEReaTISFk3PGAAkJgoewsLAXz0EdCkibqfoqTDz6+AWgoArVq1AgB07NgRoaGhGD16NF544QXUq1evxPGsWLECEyZMKHK/2yfjHT16FAsXLsSOHTuQnJwMADCZTABkcu3t7Y2AvKX1bvHz80N6enqJYyRyNyyNICIij1WpEhAfDzz9tCyVyMyUi2dkZcn7g4OBatUqWRLMO8lLik+ePFmqWMaPHw8hRJGX2x0/fhxZWVlo3749KlasiIoVK1rqhMPDw/H000/ne0xycjIqVapUqjiJ3AlHhImIyKN5ewPvvAN06AA89JAcGT5yBGjdWi7EkZLSCHv27CnyOLt27QIA3HXXXY4O2UbHjh0RHx9vc1tcXBzeffddbNiwARERETb3Xb58GSaTCQ0bNnRmmES6xESYiIgIQP/+wJ49QGys/Ld1a6BWLaBChXvwxhtv4PLly6hSpQoAoGfPnujatatl4tmuXbswa9YsDB061KYsIiEhAbGxsYiPj0dMTIxD4g4NDc137FOnTgEAOnXqlG9xjYMHD0JRFHTo0MEh8RC5EibCREQaMRqNeP311/Pdfnv7renTp8NoNDopKs/WogXwzz/Azz8DYWFA5cpAQEAMKlWqhLi4OIwcORIAEB0djS+//BKnTp2CwWBAREQEZs6ciccff9zmeHm1ulWrVnX6aylMXFwc7r33XlSuXFnrUIg0xxphIiKNGI1Gm9rP+Ph4REVF5asJZRLsXMHBskwiIkKuRufr64sRI0Zg+fLlln3efPNN/Prrr0hNTUVycjIOHTqEp59+Ol/rsn379iEmJgZNmzZ16msYM2YMhBD5RoNzcnKwatUqjBs3zqnxEOkVE2EiIqIiTJkyBQkJCfjzzz9L9Ljdu3dj0qRJDoqq5FasWIGAgAAMGzZM61CIdIGlEUREREUIDw/HggULcP78+RJNMtuyZYsDoyo5IQQWLFgAg4G//okAJsJERETF4g6jqA899JDWIRDpCksjiIiIiMgjMREmIiIiIo/ERJiIiIiIPBITYSIiIiLySEyEiYiIiMgjMREmIiIiIo/ERJiIiIiIPBITYSIiIiLySEyEiYiIiMgjMREmIiIiIo/ERJiIiIiIPBITYSIijRiNRiiKYrnExsYiMTHR5jZFUWA0GrUOlYjILTERJiLSiNFohBDCcomPj0dUVJTNbUIIJsJERA7CRJiIiIiIPBITYSIiIiLySEyEiYiIiMgjMREmIiKi/2/nfkLjKvcGjv+OBlykxfjSi9BmUUtq1RZaGFsVgmRAqlSpvCC2wgXBVoUKekujLl6Es5HqysXrxkWl4ib+wdpF88ZaOiMuCqXD2y5qkS666D//1kBTxWp47ubeuR2SeJM6k7nN8/nAgeQ5JydPfgzhy2ESyJIQBgAgS0IYAIAsCWEAALIkhAEAyJIQBgAgS0IYAIAsCWEAALIkhAFmqSzLWLZsWaxbty7WrVsXo6Oj0143NjYWq1atioGBgXjjjTfmeZcAzFZPtzcAcCPZuXNnDA8Pz3h+cnIyXnjhhfj888+jv78/1q9fH5s3b4577rlnHncJwGwIYYA2Onr0aAwMDMSKFSsiImLr1q2xf//+KSFcFMWM95juXEqpvRsFIIpO/XI9cOBA6u3t7ci9czQxMRGLFi3q9jYWBLNsn9xmuXfv3hgbG4ve3t648847Y8eOHbF48eKWa7744os4evRovPzyyxERcfDgwTh16lS89NJLLddVq9U5fe9arfbnNp+Z3F6bnWSW7WOW7XXtPIeGhmZ+uvAHOvZEuLe3N4aGhjp1++zU63XzbBOzbJ+FOMuHHnoovvnmmynrr7/+erz55puxZ8+eKIoiXnvttdi3b1+8++67Ldd9//33cfbs2eZczp49G5cvX54yp+keQtTr9RgeHo5jx4617efJ1UJ8bXaLWbaPWbZXO+bprREA1zh06NCsrnv22Wfjsccem7Le398fZ8+ebX5+7ty5WLp0adv2B0D7+K8RALN08eLF5sf79u2LNWvWTLlm/fr1cfr06Thz5kxcvXo1RkZGYvPmzfO5TQBmyRNhgFl65ZVX4vjx41EURSxfvjzeeeediIi4cOFCbN++PUZHR6OnpyfefvvtePjhh2NycjKeeeaZWL16dZd3DsB0hDDALL3//vvTri9durTlfwpv2rQpNm3aNF/bAuA6eWsEAABZEsIAAGRJCAMAkCUhDABAloQwAABZEsIAAGRJCAMAkCUhDABAloQwAABZEsIAAGRJCAN0SVmWURRF86hWq9FoNFrWiqKIsiy7vVWABUkIA3RJWZaRUmoetVotKpVKy1pKSQgDdIgQBgAgS0IYAIAsCWEAALIkhAEAyJIQBgAgS0IYAIAsCWEAALIkhAEAyJIQBgAgS0IYAIAsCWEAALIkhAEAyJIQBgAgS0IYAIAsCWEAALIkhAG6pCzLKIqieVSr1Wg0Gi1rRVFEWZbd3irAgiSEAbqkLMtIKTWPWq0WlUqlZS2lJIQBOkQIAwCQJSEMAECWhDAAAFkSwgAAZEkIAwCQJSEMAECWhDAAAFkSwgAAZEkIAwCQJSEMAECWhDAAAFkSwgAAZEkIAwCQJSEMAECWhDBAl5RlGUVRNI9qtRqNRqNlrSiKKMuy21sFWJCEMECXlGUZKaXmUavVolKptKyllIQwQIcIYQAAsiSEAQDIkhAGACBLQhgAgCwJYQAAsiSEAQDIkhAGACBLQhgAgCwJYQAAsiSEAQDIkhAGACBLQhgAgCwJYQAAsiSEAQDIkhAG6JKyLKMoiuZRrVaj0Wi0rBVFEWVZdnurAAuSEAbokrIsI6XUPGq1WlQqlZa1lJIQBugQIQwAQJaEMAAAWRLCAABkSQgDAJAlIQwAQJaEMAAAWRLCAABkSQgDAJAlIQwAQJaEMAAAWerp9gYAbgRbtmyJr7/+OiIixsfHo6+vL44fPz7luuXLl8fixYvj5ptvjp6enjh27Nh8bxWAWRLCALPwwQcfND/etWtX3HrrrTNeW6vVYsmSJfOxLQD+BCEMMAcppfjwww/j8OHD3d4KAH+SEAaYgy+//DJuv/32WLly5bTni6KIjRs3RlEU8fzzz8dzzz0343Uzme5cSun6NgzAjIpO/XI9cOBA6u3t7ci9czQxMRGLFi3q9jYWBLNsn4U2y127dsWlS5emrG/bti0GBwcjIuKtt96KZcuWxZNPPjntPX744YdYsmRJ/PTTTzE8PBwvvvhirF27dsp11Wp1Tnur1Wpzuj53C+212U1m2T5m2V7XznNoaGjmpwt/oGNPhHt7e2NoaKhTt89OvV43zzYxy/ZZaLNsNBp/eP7333+PLVu2RKPRiP7+/n97vxMnTsRvv/027YymewhRr9djeHjYH9i1wUJ7bXaTWbaPWbZXO+bp36cBzNKhQ4firrvumjGCr1y5EpcvX25+fPDgwVizZs18bhGAORDCALM0MjISTz31VMvahQsXYtOmTRER8e2338bg4GCsXbs2NmzYEI8++mg88sgj3dgqALPgj+UAZmnv3r1T1pYuXRqjo6MREbFixYo4ceLEPO8KgOvliTAAAFkSwgAAZEkIAwCQJSEMAECWhDAAAFkSwgAAZEkIAwCQJSEMAECWhDAAAFkSwgAAZEkIAwCQJSEM0CVlWUZRFM2jWq1Go9FoWSuKIsqy7PZWARYkIQzQJWVZRkqpedRqtahUKi1rKSUhDNAhQhgAgCwJYQAAsiSEAQDIkhAGACBLQhgAgCwJYQAAsiSEAQDIkhAGACBLQhgAgCwJYQAAsiSEAQDIkhAGACBLQhgAgCwJYQAAsiSEAbqkLMsoiqJ5VKvVaDQaLWtFUURZlt3eKsCCJIQBuqQsy0gpNY9arRaVSqVlLaUkhAE6RAgDAJAlIQwAQJaEMAAAWRLCAABkSQgDAJAlIQwAQJaEMAAAWRLCAABkSQgDAJAlIQwAQJaEMAAAWRLCAABkSQgDAJAlIQwAQJaEMAAAWRLCAF1SlmUURdE8qtVqNBqNlrWiKKIsy25vFWBBEsIAXVKWZaSUmketVotKpdKyllISwgAdIoQBAMiSEAYAIEtCGACALAlhAACyJIQBAMiSEAYAIEtCGACALAlhAACyJIQBAMiSEAYAIEtCGACALAlhAACyJIQBAMiSEAYAIEtCGKBLyrKMoiiaR7VajUaj0bJWFEWUZdntrQIsSEIYoEvKsoyUUvOo1WpRqVRa1lJKQhigQ4QwAABZEsIAAGRJCAMAkCUhDABAloQwAABZEsIAAGRJCAMAkCUhDABAloQwAABZEsIAAGRJCANc46OPPorVq1fHTTfdFMeOHWs5t3v37hgYGIhVq1bFZ599Nu3XnzlzJu67775YuXJlbNmyJa5evTof2wbgOghhgGusWbMmPvnkk3jwwQdb1r/66qsYGRmJkydPxtjYWOzYsSMmJyenfP2rr74aO3fujNOnT8dtt90We/bsma+tAzBHQhjgGnfffXesWrVqyvr+/ftj69atccstt8Qdd9wRAwMDcfTo0ZZrUkpx+PDheOKJJyIi4umnn45PP/10XvYNwNz1dHsDADeC8+fPx/3339/8vL+/P86fP99yzY8//hh9fX3R09Mz4zX/VBTFjN9runMppevZNgB/oGMhfOXKlajX6526fXYmJibMs03Msn1u1Fnu2rUrLl26NGV927ZtMTg4GBER4+Pj0Wg0YmJiIiIizp07F6dOnWr+vBcvXoyTJ0/GkiVLml8/Pj4ev/zyS/Oa7777Ln7++ee2zOhGnHM33aivzf9EZtk+Ztle185zaGjouu7RsRDu7e297k0xVb1eN882Mcv2uVFn2Wg0/u01fX19UalU4t57742IiCNHjkTEv37Z7t69OzZu3BgPPPBA82tSSrF9+/YYHByMnp6eOHLkSKxcuXLaGU33hLder8fw8PCUP9Jj7m7U1+Z/IrNsH7Nsr3bM03uEAWZh8+bNMTIyEr/++mucOXMmTp8+HRs2bGi5piiKqFar8fHHH0dExHvvvRePP/54N7YLwCwU3ncG8C9FUfx3RPxvRPwlIsYj4nhK6eF/nPufiHgmIn6PiL+llP7vH+ujEbE9pXShKIoVETESEf8VEf8fEX9NKf06h+8/llJ6pJ0/EwDTE8IAAGTJWyMAAMiSEAYAIEtCGACALAlhAACyJIQBAMiSEAYAIEtCGACALAlhAACy9HdFu7TVva8s3AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 12))\n",
    "\n",
    "vects = np.array([[2, 9], [-3, 4], [3, -4], [5, 5]])\n",
    "col = ['red', 'blue', 'blue', 'green']\n",
    "cordt = ['$(2, 9)$', '$(-3, 4)$', '$(3, -4)$', '$(5, 5)$']\n",
    "\n",
    "for i in range(4):\n",
    "    ax.arrow(0, 0, vects[i, 0], vects[i, 1], color = col[i], width = .08, \n",
    "             length_includes_head = True,\n",
    "             head_width = .3, # default: 3*width\n",
    "             head_length = .6,\n",
    "             overhang = .4)\n",
    "    ax.text(x = vects[i][0], y = vects[i][1], s = cordt[i], size = 15)\n",
    "ax.grid()\n",
    "\n",
    "points = np.array([[2, 9], [5, 5], [3, -4], [-3, 4]])\n",
    "\n",
    "ax.arrow(points[3][0], points[3][1], points[1][0], points[1][1], color = 'green', width = .08, \n",
    "         length_includes_head = True,\n",
    "         head_width = .3, # default: 3*width\n",
    "         head_length = .6,\n",
    "         overhang = .4)\n",
    "\n",
    "line1 = np.array([points[0], points[1]])\n",
    "ax.plot(line1[:,0], line1[:,1], c = 'b', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line2 = np.array([points[2], points[1]])\n",
    "ax.plot(line2[:,0], line2[:,1], c = 'b', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "ax.text(-2, 6, '$\\|\\|\\mathbf{u}-\\mathbf{v}\\|\\|$', size = 16)\n",
    "\n",
    "###################### Axis, Spines, Ticks ##########################\n",
    "ax.axis([-10, 10.1, -10.1, 10.1])\n",
    "ax.spines['left'].set_position('center')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position('center')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "ax.minorticks_on()\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=12, width=2, which='major')\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=10, width=1, which='minor')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the graph, we know that the $\\|\\mathbf{u}-\\mathbf{v}\\|$ is $\\sqrt{5^2 + 5^2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 7.0710678118654755$"
      ],
      "text/plain": [
       "7.0710678118654755"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(5**2 + 5**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same results as the ```np.linalg.norm(u - v)```."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Orthogonal Vectors</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have two vectors $\\mathbf{u}$ and $\\mathbf{v}$, and square the distance of $\\|\\mathbf{u}+\\mathbf{v}\\|$ and $\\|\\mathbf{u}-\\mathbf{v}\\|$ \n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\big[\\operatorname{dist}(\\mathbf{u},-\\mathbf{v})\\big]^{2} &=\\|\\mathbf{u}-(-\\mathbf{v})\\|^{2}=\\|\\mathbf{u}+\\mathbf{v}\\|^{2} \\\\\n",
    "&=(\\mathbf{u}+\\mathbf{v}) \\cdot(\\mathbf{u}+\\mathbf{v}) \\\\\n",
    "&=\\mathbf{u} \\cdot(\\mathbf{u}+\\mathbf{v})+\\mathbf{v} \\cdot(\\mathbf{u}+\\mathbf{v}) \\\\\n",
    "&=\\mathbf{u} \\cdot \\mathbf{u}+\\mathbf{u} \\cdot \\mathbf{v}+\\mathbf{v} \\cdot \\mathbf{u}+\\mathbf{v} \\cdot \\mathbf{v} \\\\\n",
    "&=\\|\\mathbf{u}\\|^{2}+\\|\\mathbf{v}\\|^{2}+2 \\mathbf{u} \\cdot \\mathbf{v}\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{aligned}\n",
    "\\big[\\operatorname{dist}(\\mathbf{u}, \\mathbf{v})\\big]^{2} &=\\|\\mathbf{u}\\|^{2}+\\|-\\mathbf{v}\\|^{2}+2 \\mathbf{u} \\cdot(-\\mathbf{v}) \\\\\n",
    "&=\\|\\mathbf{u}\\|^{2}+\\|\\mathbf{v}\\|^{2}-2 \\mathbf{u} \\cdot \\mathbf{v}\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose $\\mathbf{u} = (1, 4)$ and $\\mathbf{v} = (-2, 2)$, visualize the vector and distances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 12))\n",
    "\n",
    "vects = np.array([[1, 4], [-2, 2], [2, -2]])\n",
    "colr = ['red', 'blue', 'blue'] \n",
    "cordt = ['$(1, 4)$', '$(-2, 2)$', '$(2, -2)$']\n",
    "vec_name = ['$\\mathbf{u}$', '$\\mathbf{v}$','$\\mathbf{-v}$']\n",
    "\n",
    "for i in range(3):\n",
    "    ax.arrow(0, 0, vects[i][0], vects[i][1], color = colr[i], width = .08, \n",
    "             length_includes_head = True,\n",
    "             head_width = .3, # default: 3*width\n",
    "             head_length = .6,\n",
    "             overhang = .4)\n",
    "    ax.text(x = vects[i][0], y = vects[i][1], s = cordt[i], size = 15)\n",
    "    ax.text(x = vects[i][0]/2, y = vects[i][1]/2, s = vec_name[i], size = 22)\n",
    "\n",
    "ax.text(x = -1, y = 3, s = '$\\|\\|\\mathbf{u}-\\mathbf{v}\\|\\|$', size = 15)    \n",
    "ax.text(x = 1.5, y = 1, s = '$\\|\\|\\mathbf{u}+\\mathbf{v}\\|\\|$', size = 15)    \n",
    "\n",
    "\n",
    "\n",
    "############################### Dashed Line #######################\n",
    "line1 = np.array([vects[0], vects[1]])\n",
    "ax.plot(line1[:,0], line1[:,1], c = 'b', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line2 = np.array([vects[0], vects[2]])\n",
    "ax.plot(line2[:,0], line2[:,1], c = 'b', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "###################### Axis, Spines, Ticks ##########################\n",
    "ax.spines['left'].set_position('center')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position('center')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "ax.minorticks_on()\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=12, width=2, which='major')\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=10, width=1, which='minor')\n",
    "\n",
    "ax.axis([-5, 5, -5, 5])\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that if $\\big[\\operatorname{dist}(\\mathbf{u},-\\mathbf{v})\\big]^{2} = \\big[\\operatorname{dist}(\\mathbf{u}, \\mathbf{v})\\big]^{2}$, $\\mathbf{u}$ and $\\mathbf{v}$ are orthogonal.According to equations above, it must be \n",
    "\n",
    "$$\\mathbf{u} \\cdot \\mathbf{v} = 0$$\n",
    "\n",
    "This is one of the most important conclusion in linear algebra."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose there is another vector $w = (2.5, 2.5)$, let's plot over the graph again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 12))\n",
    "\n",
    "vects = np.array([[1, 4], [-2, 2], [2, -2], [2.5, 2.5]])\n",
    "colr = ['red', 'blue', 'blue', 'green'] \n",
    "cordt = ['$(1, 4)$', '$(-2, 2)$', '$(2, -2)$', '$(2.5, 2.5)$']\n",
    "vec_name = ['$\\mathbf{u}$', '$\\mathbf{v}$','$\\mathbf{-v}$', '$\\mathbf{w}$']\n",
    "\n",
    "for i in range(4):\n",
    "    ax.arrow(0, 0, vects[i][0], vects[i][1], color = colr[i], width = .08, \n",
    "             length_includes_head = True,\n",
    "             head_width = .3, # default: 3*width\n",
    "             head_length = .6,\n",
    "             overhang = .4)\n",
    "    ax.text(x = vects[i][0], y = vects[i][1], s = cordt[i], size = 15)\n",
    "    ax.text(x = vects[i][0]/2, y = vects[i][1]/2, s = vec_name[i], size = 22)\n",
    "\n",
    "ax.text(x = -1, y = 3, s = '$\\|\\|\\mathbf{u}-\\mathbf{v}\\|\\|$', size = 15)    \n",
    "ax.text(x = 1.5, y = 1, s = '$\\|\\|\\mathbf{u}+\\mathbf{v}\\|\\|$', size = 15)    \n",
    "\n",
    "############################### Dashed Line #######################\n",
    "\n",
    "line1 = np.array([vects[0], vects[1]])\n",
    "ax.plot(line1[:,0], line1[:,1], c = 'b', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line2 = np.array([vects[0], vects[2]])\n",
    "ax.plot(line2[:,0], line2[:,1], c = 'b', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line1 = np.array([vects[1], vects[3]])\n",
    "ax.plot(line1[:,0], line1[:,1], c = 'k', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line2 = np.array([vects[2], vects[3]])\n",
    "ax.plot(line2[:,0], line2[:,1], c = 'k', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "###################### Axis, Spines, Ticks ##########################\n",
    "ax.spines['left'].set_position('center')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position('center')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "ax.minorticks_on()\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=12, width=2, which='major')\n",
    "ax.tick_params(axis = 'both', direction = 'inout', length=10, width=1, which='minor')\n",
    "\n",
    "ax.axis([-5, 5, -5, 5])\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use SciPy built-in function, construct two $2\\times 2$ matrices for holding head and tail coordinates of the vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1, 4], [-2, 2]])\n",
    "b = np.array([[1, 4], [2, -2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.60555128])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance = sp.spatial.distance.pdist(a, 'euclidean'); distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.08276253])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance = sp.spatial.distance.pdist(b, 'euclidean');distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verify by NumPy ```.norm```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dist(u, v):\n",
    "    a = np.linalg.norm(u - v)\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3.605551275463989$"
      ],
      "text/plain": [
       "3.605551275463989"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = np.array([1, 4])\n",
    "v = np.array([-2, 2])\n",
    "dist(u, v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 6.082762530298219$"
      ],
      "text/plain": [
       "6.082762530298219"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = np.array([1, 4])\n",
    "v = np.array([2, -2])\n",
    "dist(u, v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now Let's test if vector $(2.5, 2.5)^T$ is perpendicular to $(2, -2)^T$ and $(-2, 2)^T$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[2.5, 2.5], [-2, 2]])\n",
    "b = np.array([[2.5, 2.5], [2, -2]])\n",
    "distance1 = sp.spatial.distance.pdist(a, 'euclidean')\n",
    "distance2 = sp.spatial.distance.pdist(b, 'euclidean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.52769257] [4.52769257]\n"
     ]
    }
   ],
   "source": [
    "print(distance1, distance2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They are the same length, which means $\\mathbf{w}\\perp \\mathbf{v}$ and $\\mathbf{w}\\perp \\mathbf{-v}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Orthogonal Complements</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, the set of all vectors $\\mathbf{z}$ that are orthogonal to subspace $W$ is called <font face=\"gotham\" color=\"red\"> orthogonal complement</font>, or denoted as $W^\\perp$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most common example would be \n",
    "\n",
    "$$(\\operatorname{Row} A)^{\\perp}=\\operatorname{Nul} A \\quad \\text { and } \\quad(\\operatorname{Col} A)^{\\perp}=\\operatorname{Nul} A^{T}$$\n",
    "\n",
    "The nullspace of $A$ is perpendicular to the row space of $A$; the nullspace of $A^T$ is perpendicular to the column space of $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Angles in $\\mathbb{R}^n$</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is one formula of calculating angles in vector space, to derive it we need the law of cosine:\n",
    "\n",
    "$$\\|\\mathbf{u}-\\mathbf{v}\\|^{2}=\\|\\mathbf{u}\\|^{2}+\\|\\mathbf{v}\\|^{2}-2\\|\\mathbf{u}\\|\\|\\mathbf{v}\\| \\cos \\vartheta$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rearrange, we get\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\|\\mathbf{u}\\|\\|\\mathbf{v}\\| \\cos \\vartheta &=\\frac{1}{2}\\left[\\|\\mathbf{u}\\|^{2}+\\|\\mathbf{v}\\|^{2}-\\|\\mathbf{u}-\\mathbf{v}\\|^{2}\\right] \\\\\n",
    "&=\\frac{1}{2}\\left[u_{1}^{2}+u_{2}^{2}+v_{1}^{2}+v_{2}^{2}-\\left(u_{1}-v_{1}\\right)^{2}-\\left(u_{2}-v_{2}\\right)^{2}\\right] \\\\\n",
    "&=u_{1} v_{1}+u_{2} v_{2} \\\\\n",
    "&=\\mathbf{u} \\cdot \\mathbf{v}\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In statistics, $\\cos{\\vartheta}$ is called <font face=\"gotham\" color=\"red\"> correlation coefficient </font>.\n",
    "\n",
    "$$\n",
    "\\cos{\\vartheta}=\\frac{\\mathbf{u} \\cdot \\mathbf{v}}{\\|\\mathbf{u}\\|\\|\\mathbf{v}\\|}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Geometric Interpretation of Dot Product</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You probably have notices that sometimes <i>dot product</i> and <i>inner product</i> are used interchangeably. Despite that, they do have different meanings. \n",
    "\n",
    "Functions and polynomials can have inner product as well, but we usually use dot product to refer to inner product among vector space.\n",
    "\n",
    "We will show that dot product has an interesting geometric interpretation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider two vectors $\\mathbf{a}$ and $\\mathbf{u}$, pointing different direction, the angle form by them is $\\vartheta$, also $\\mathbf{u}$ is a unit vector. We would like to know how much $\\mathbf{a}$ is pointing to $\\mathbf{u}$'s direction.\n",
    "\n",
    "And this value can be calculated by projecting $\\mathbf{a}$ onto $\\mathbf{u}$,\n",
    "\n",
    "$$\n",
    " \\|\\mathbf{a}\\|\\cos{\\vartheta}=\\|\\mathbf{a}\\| \\|\\mathbf{u}\\|\\cos{\\vartheta} = \\mathbf{a} \\cdot\\mathbf{u} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any vector $\\mathbf{b}$ can be normalized as a unit vector $\\mathbf{u}$, then perform the calculation above, we can tell how much $\\mathbf{b}$ is pointing the direction of $\\mathbf{u}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Orthogonal Sets</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a set of vectors $S = \\left\\{\\mathbf{u}_{1}, \\ldots, \\mathbf{u}_{p}\\right\\}$ in $\\mathbb{R}^{n}$ has any arbitrary pair to be orthogonal, i.e. $\\mathbf{u}_{i} \\cdot \\mathbf{u}_{j}=0$ whenever $i \\neq j$, $S =\\left\\{\\mathbf{u}_{1}, \\ldots, \\mathbf{u}_{p}\\right\\}$ is called an <font face=\"gotham\" color=\"red\">orthogonal set</font>. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naturally, orthogonal set $S$ is linearly independent, they are also an <font face=\"gotham\" color=\"red\"> orthogonal basis</font> for space spanned by $\\left\\{\\mathbf{u}_{1}, \\ldots, \\mathbf{u}_{p}\\right\\}$. Orthogonal basis has an advantage is that coordinates of the basis can be quickly computed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For instance any $\\mathbf{y}$ in $W$, \n",
    "\n",
    "$$\n",
    "\\mathbf{y}=c_{1} \\mathbf{u}_{1}+\\cdots+c_{p} \\mathbf{u}_{p}\n",
    "$$\n",
    "\n",
    "Because it is an orthogonal sets,\n",
    "\n",
    "$$\n",
    "\\mathbf{y} \\cdot \\mathbf{u}_{1}=\\left(c_{1} \\mathbf{u}_{1}+c_{2} \\mathbf{u}_{2}+\\cdots+c_{p} \\mathbf{u}_{p}\\right) \\cdot \\mathbf{u}_{1}=c_{1}\\left(\\mathbf{u}_{1} \\cdot \\mathbf{u}_{1}\\right)\n",
    "$$\n",
    "\n",
    "Thus\n",
    "\n",
    "$$c_{j}=\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{j}}{\\mathbf{u}_{j} \\cdot \\mathbf{u}_{j}} \\quad(j=1, \\ldots, p)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Orthogonal Projection</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any $\\mathbf{y}$ in $\\mathbb{R}^n$, we want to decompose it as \n",
    "\n",
    "$$\n",
    "\\mathbf{y} = \\alpha \\mathbf{u}+\\mathbf{z} = \\hat{\\mathbf{y}}+\\mathbf{z}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $ \\mathbf{u}$ is perpendicular to $\\mathbf{z}$, $\\alpha$ is a scalar.And the subspace $L$ spanned by $\\mathbf{u}$, the projection of $\\mathbf{y}$ onto $L$ is denoted as\n",
    "\n",
    "$$\\hat{\\mathbf{y}}=\\operatorname{proj}_{L} \\mathbf{y}=\\frac{\\mathbf{y} \\cdot \\mathbf{u}}{\\mathbf{u} \\cdot \\mathbf{u}} \\mathbf{u}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Becasue $\\mathbf{u}\\perp \\mathbf{z}$, then $\\mathbf{u}\\cdot \\mathbf{z} = 0$, replace $\\mathbf{z}$ by $\\mathbf{y}- \\alpha \\mathbf{u}$:\n",
    "\n",
    "$$\n",
    "(\\mathbf{y}- \\alpha \\mathbf{u})\\cdot \\mathbf{u}= 0\\\\\n",
    "\\alpha = \\frac{\\mathbf{y}\\cdot \\mathbf{u}}{\\mathbf{u}\\cdot \\mathbf{u}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we get the formula for projection onto $L$ spanned by $\\mathbf{u}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> A Visual Example in $\\mathbb{R}^T$</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have $\\mathbf{y} = (2, 5)^T$, $\\mathbf{u} = (3, 1)^T$. Plot $\\hat{\\mathbf{y}}$ onto the subspace spanned $L$ by $\\mathbf{u}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 12))\n",
    "\n",
    "vects = np.array([[4, 5], [2, 1]])\n",
    "colr = ['red', 'blue'] \n",
    "cordt = ['$(4, 5)$', '$(2, 1)$']\n",
    "vec_name = ['$\\mathbf{y}$', '$\\mathbf{u}$']\n",
    "\n",
    "for i in range(2):\n",
    "    ax.arrow(0, 0, vects[i][0], vects[i][1], color = colr[i], width = .03, \n",
    "             length_includes_head = True,\n",
    "             head_width = .1, # default: 3*width\n",
    "             head_length = .2,\n",
    "             overhang = .4)\n",
    "    ax.text(x = vects[i][0], y = vects[i][1], s = cordt[i], size = 15)\n",
    "    ax.text(x = vects[i][0]/2, y = vects[i][1]/2, s = vec_name[i], size = 22)\n",
    "\n",
    "################################### Subspace L ############################\n",
    "x = np.linspace(0, 8.1)\n",
    "y = 1/2*x\n",
    "ax.plot(x, y, lw = 3, color = 'red', alpha = .5)\n",
    "ax.text(x = 6.5, y = 3, s = '$L = \\operatorname{Span(\\mathbf{u})}$', size = 19)\n",
    "\n",
    "ax.axis([0, 8, 0, 8])\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use formula to compute $\\alpha$ and $\\hat{\\mathbf{y}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2.6$"
      ],
      "text/plain": [
       "2.6"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.array([4, 5])\n",
    "u = np.array([2, 1])\n",
    "alpha = (y@u)/(u@u);alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.2, 2.6])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = alpha*u;yhat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With results above, we can plot the orthogonal projection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 12))\n",
    "\n",
    "vects = np.array([[4, 5], [2, 1], [5.2, 2.6]])\n",
    "colr = ['red', 'blue', 'green'] \n",
    "cordt = ['$(4, 5)$', '$(2, 1)$', '(5.2, 2.6)']\n",
    "vec_name = ['$\\mathbf{y}$', '$\\mathbf{u}$', r'$\\hat{\\mathbf{y}} = \\alpha\\mathbf{u}$']\n",
    "\n",
    "for i in range(3):\n",
    "    ax.arrow(0, 0, vects[i][0], vects[i][1], color = colr[i], width = .03, \n",
    "             length_includes_head = True,\n",
    "             head_width = .1, # default: 3*width\n",
    "             head_length = .2,\n",
    "             overhang = .4, zorder = -i)\n",
    "    ax.text(x = vects[i][0], y = vects[i][1], s = cordt[i], size = 19)\n",
    "    ax.text(x = vects[i][0]/2, y = vects[i][1]/2, s = vec_name[i], size = 22)\n",
    "\n",
    "##################################### Components of y orthogonal to u ##########################\n",
    "\n",
    "point1 = [4, 5]\n",
    "point2 = [5.2, 2.6]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], c = 'k', lw = 3.5,alpha =0.5, ls = '--')\n",
    "ax.text(4.7, 3.8, '$\\mathbf{z}$', size = 22)\n",
    "################################### Subspace L ############################\n",
    "x = np.linspace(0, 8.1)\n",
    "y = 1/2*x\n",
    "ax.plot(x, y, lw = 3, color = 'red', alpha = .5, zorder = -3)\n",
    "ax.text(x = 6.5, y = 3, s = '$L = \\operatorname{Span(\\mathbf{u})}$', size = 19)\n",
    "\n",
    "ax.axis([0, 8, 0, 8])\n",
    "ax.grid()\n",
    "\n",
    "#################################### Formula ################################\n",
    "ax.text(x = 1, y = 7, \n",
    "        s = r'$(\\mathbf{y}- \\alpha \\mathbf{u})\\cdot \\mathbf{u}= 0$',\n",
    "        size = 22, color = 'b')\n",
    "ax.text(x = 1, y = 6.5, \n",
    "        s = r'$\\alpha = \\frac{\\mathbf{y}\\cdot \\mathbf{u}}{\\mathbf{u}\\cdot \\mathbf{u}}$',\n",
    "        size = 22, color = 'b')\n",
    "ax.text(x = 1, y = 6, \n",
    "        s = r'$\\operatorname{proj}_{L}\\mathbf{y}=\\frac{\\mathbf{y}\\cdot\\mathbf{u}}{\\mathbf{u}\\cdot\\mathbf{u}}\\mathbf{u}$',\n",
    "        size = 22, color = 'b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> The Orthogonal Decomposition Theorem</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generalize the orthogonal projection in the higher dimension $\\mathbb{R}^n$, we summarize the idea into the <font face=\"gotham\" color=\"red\"> orthogonal decomposition theorem</font>.\n",
    "\n",
    "Let $W$ be a subspace of $\\mathbb{R}^{n}$. Then each $\\mathbf{y}$ in $\\mathbb{R}^{n}$ can be written uniquely in the form\n",
    "$$\n",
    "\\mathbf{y}=\\hat{\\mathbf{y}}+\\mathbf{z}\n",
    "$$\n",
    "where $\\hat{\\mathbf{y}}$ is in $W$ and $\\mathbf{z}$ is in $W^{\\perp} .$ In fact, if $\\left\\{\\mathbf{u}_{1}, \\ldots, \\mathbf{u}_{p}\\right\\}$ is any orthogonal basis of $W,$ then\n",
    "$$\n",
    "\\hat{\\mathbf{y}}=\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{1}}{\\mathbf{u}_{1} \\cdot \\mathbf{u}_{1}} \\mathbf{u}_{1}+\\cdots+\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{p}}{\\mathbf{u}_{p} \\cdot \\mathbf{u}_{p}} \\mathbf{u}_{p}\n",
    "$$\n",
    "and $\\mathbf{z}=\\mathbf{y}-\\hat{\\mathbf{y}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In $\\mathbb{R}^{2}$, we project $\\mathbf{y}$ onto subspace $L$ which is spanned by $\\mathbf{u}$, here we generalize the formula for $\\mathbb{R}^{n}$, that $\\mathbf{y}$ is projected onto $W$ which is spanned by $\\left\\{\\mathbf{u}_{1}, \\ldots, \\mathbf{u}_{p}\\right\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> A Visual Example in $\\mathbb{R}^{3}$</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A subspace $W=\\operatorname{Span}\\left\\{\\mathbf{u}_{1}, \\mathbf{u}_{2}\\right\\}$, and a vector $\\mathbf{y}$ is not in $W$, decompose $\\mathbf{y}$ into $\\hat{\\mathbf{y}} + \\mathbf{z}$, and plot them.\n",
    "\n",
    "where \n",
    "\n",
    "$$\\mathbf{u}_{1}=\\left[\\begin{array}{r}\n",
    "2 \\\\\n",
    "5 \\\\\n",
    "-1\n",
    "\\end{array}\\right], \\mathbf{u}_{2}=\\left[\\begin{array}{r}\n",
    "-2 \\\\\n",
    "1 \\\\\n",
    "1\n",
    "\\end{array}\\right], \\text { and } \\mathbf{y}=\\left[\\begin{array}{l}\n",
    "1 \\\\\n",
    "2 \\\\\n",
    "3\n",
    "\\end{array}\\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The projection onto $W$ in $\\mathbb{R}^3$ is \n",
    "\n",
    "$$\n",
    "\\hat{\\mathbf{y}}=\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{1}}{\\mathbf{u}_{1} \\cdot \\mathbf{u}_{1}} \\mathbf{u}_{1}+\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{2}}{\\mathbf{u}_{2} \\cdot \\mathbf{u}_{2}} \\mathbf{u}_{2}=\\hat{\\mathbf{y}}_{1}+\\hat{\\mathbf{y}}_{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The codes for plotting are quite redundent, however exceedingly intuitive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"682\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "######################## Subspace W ##############################\n",
    "s = np.linspace(-.5, .5, 10)\n",
    "t = np.linspace(-.5, .5, 10)\n",
    "S, T = np.meshgrid(s, t)\n",
    "\n",
    "X1 = 2 * S - 2 * T\n",
    "X2 = 5 * S + T\n",
    "X3 = -S + T\n",
    "\n",
    "fig = plt.figure(figsize = (7, 7))\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.plot_wireframe(X1, X2, X3, linewidth = 1.5, alpha = .3)\n",
    "\n",
    "########################### vector y ###############################\n",
    "y = np.array([1, 2, 3])\n",
    "u1, u2 = np.array([2, 5, -1]), np.array([-2, 1, 1])\n",
    "\n",
    "vec = np.array([[0, 0, 0, y[0], y[1], y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "ax.text(y[0], y[1], y[2], '$\\mathbf{y}$', size = 15)\n",
    "########################### vector u1 and u2 ###############################\n",
    "\n",
    "vec = np.array([[0, 0, 0, u1[0], u1[1], u1[2]]])\n",
    "X, Y, Z, U, V, W = zip(*vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "vec = np.array([[0, 0, 0, u2[0], u2[1], u2[2]]])\n",
    "X, Y, Z, U, V, W = zip(*vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "\n",
    "ax.text(u1[0], u1[1], u1[2], '$\\mathbf{u}_1$', size = 15)\n",
    "ax.text(u2[0], u2[1], u2[2], '$\\mathbf{u}_2$', size = 15)\n",
    "###########################  yhat ###############################\n",
    "\n",
    "alpha1 = (y@u1)/(u1@u1)\n",
    "alpha2 = (y@u2)/(u2@u2)\n",
    "\n",
    "yhat1 = alpha1*u1\n",
    "yhat2 = alpha2*u2\n",
    "yhat = yhat1 + yhat2\n",
    "\n",
    "vec = np.array([[0, 0, 0, yhat1[0], yhat1[1], yhat1[2]]])\n",
    "X, Y, Z, U, V, W = zip(*vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'blue', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3, zorder= 3)\n",
    "\n",
    "vec = np.array([[0, 0, 0, yhat2[0], yhat2[1], yhat2[2]]])\n",
    "X, Y, Z, U, V, W = zip(*vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'blue', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3, zorder= 3)\n",
    "\n",
    "vec = np.array([[0, 0, 0, yhat[0], yhat[1], yhat[2]]])\n",
    "X, Y, Z, U, V, W = zip(*vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'pink', alpha = 1,arrow_length_ratio = .12, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3, zorder= 3)\n",
    "\n",
    "ax.text(yhat1[0], yhat1[1], yhat1[2], '$\\hat{\\mathbf{y}}_1$', size = 15)\n",
    "ax.text(yhat2[0], yhat2[1], yhat2[2], '$\\hat{\\mathbf{y}}_2$', size = 15)\n",
    "ax.text(x = yhat[0], y = yhat[1], z = yhat[2], \n",
    "        s = r'$\\hat{\\mathbf{y}}=\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{1}}{\\mathbf{u}_{1} \\cdot \\mathbf{u}_{1}} \\mathbf{u}_{1}+\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{2}}{\\mathbf{u}_{2} \\cdot \\mathbf{u}_{2}} \\mathbf{u}_{2}=\\hat{\\mathbf{y}}_{1}+\\hat{\\mathbf{y}}_{2}$', size = 15)\n",
    "###########################  z ###############################\n",
    "z = y - yhat\n",
    "vec = np.array([[yhat[0], yhat[1], yhat[2], z[0], z[1], z[2]]])\n",
    "X, Y, Z, U, V, W = zip(*vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'green', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "############################ Dashed Line ####################\n",
    "\n",
    "line1 = np.array([y, yhat1])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:,2], c = 'b', lw = 3.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line2 = np.array([y, yhat2])\n",
    "ax.plot(line2[:,0], line2[:,1], line2[:,2], c = 'b', lw = 2.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line3 = np.array([yhat, yhat2])\n",
    "ax.plot(line3[:,0], line3[:,1], line3[:,2], c = 'b', lw = 2.5,alpha =0.5, ls = '--')\n",
    "\n",
    "line4 = np.array([yhat, yhat1])\n",
    "ax.plot(line4[:,0], line4[:,1], line4[:,2], c = 'b', lw = 2.5,alpha =0.5, ls = '--')\n",
    "\n",
    "############################# View Angel\n",
    "ax.view_init(elev=-6, azim=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Orthonormal Sets</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An <font face=\"gotham\" color=\"red\"> orthonormal set</font> is obtained from normalizing the orthogonal set, and also called <font face=\"gotham\" color=\"red\">orthonomal basis</font>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrices whose columns form an orthonormal set are important for matrix computation.\n",
    "\n",
    "Let $U=\\left[\\begin{array}{lll}\n",
    "\\mathbf{u}_{1} & \\mathbf{u}_{2} & \\mathbf{u}_{3}\n",
    "\\end{array}\\right]$, where $\\mathbf{u}_{i}$'s are from an orthonormal set, the outer product, $U^TU$ is\n",
    "\n",
    "$$U^{T} U=\\left[\\begin{array}{l}\n",
    "\\mathbf{u}_{1}^{T} \\\\\n",
    "\\mathbf{u}_{2}^{T} \\\\\n",
    "\\mathbf{u}_{3}^{T}\n",
    "\\end{array}\\right]\\left[\\begin{array}{lll}\n",
    "\\mathbf{u}_{1} & \\mathbf{u}_{2} & \\mathbf{u}_{3}\n",
    "\\end{array}\\right]=\\left[\\begin{array}{lll}\n",
    "\\mathbf{u}_{1}^{T} \\mathbf{u}_{1} & \\mathbf{u}_{1}^{T} \\mathbf{u}_{2} & \\mathbf{u}_{1}^{T} \\mathbf{u}_{3} \\\\\n",
    "\\mathbf{u}_{2}^{T} \\mathbf{u}_{1} & \\mathbf{u}_{2}^{T} \\mathbf{u}_{2} & \\mathbf{u}_{2}^{T} \\mathbf{u}_{3} \\\\\n",
    "\\mathbf{u}_{3}^{T} \\mathbf{u}_{1} & \\mathbf{u}_{3}^{T} \\mathbf{u}_{2} & \\mathbf{u}_{3}^{T} \\mathbf{u}_{3}\n",
    "\\end{array}\\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And $\\mathbf{u}_{i}^{T} \\mathbf{u}_{j}, i, j \\in (1, 2, 3)$ is an inner product."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of orthonormal sets, we have \n",
    "\n",
    "$$\n",
    "\\mathbf{u}_{1}^{T} \\mathbf{u}_{2}=\\mathbf{u}_{2}^{T} \\mathbf{u}_{1}=0, \\quad \\mathbf{u}_{1}^{T} \\mathbf{u}_{3}=\\mathbf{u}_{3}^{T} \\mathbf{u}_{1}=0, \\quad \\mathbf{u}_{2}^{T} \\mathbf{u}_{3}=\\mathbf{u}_{3}^{T} \\mathbf{u}_{2}=0\\\\\n",
    "\\mathbf{u}_{1}^{T} \\mathbf{u}_{1}=1, \\quad \\mathbf{u}_{2}^{T} \\mathbf{u}_{2}=1, \\quad \\mathbf{u}_{3}^{T} \\mathbf{u}_{3}=1\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which means\n",
    "\n",
    "$$\n",
    "U^TU = I\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that we have a general projection formula \n",
    "\n",
    "$$\n",
    "\\hat{\\mathbf{y}}=\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{1}}{\\mathbf{u}_{1} \\cdot \\mathbf{u}_{1}} \\mathbf{u}_{1}+\\cdots+\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{p}}{\\mathbf{u}_{p} \\cdot \\mathbf{u}_{p}} \\mathbf{u}_{p}\n",
    "=\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{1}}{{\\mathbf{u}_{1}^T} \\mathbf{u}_{1}} \\mathbf{u}_{1}+\\cdots+\\frac{\\mathbf{y} \\cdot \\mathbf{u}_{p}}{{\\mathbf{u}_{p}^T} \\mathbf{u}_{p}} \\mathbf{u}_{p}\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the $\\{\\mathbf{u}_1,...,\\mathbf{u}_p\\}$ is an orthonormal set, then \n",
    "\n",
    "\\begin{align}\n",
    "\\hat{\\mathbf{y}}&=\\left(\\mathbf{y} \\cdot \\mathbf{u}_{1}\\right) \\mathbf{u}_{1}+\\left(\\mathbf{y} \\cdot \\mathbf{u}_{2}\\right) \\mathbf{u}_{2}+\\cdots+\\left(\\mathbf{y} \\cdot \\mathbf{u}_{p}\\right) \\mathbf{u}_{p}\\\\\n",
    "& = \\left(\\mathbf{u}_{1}^T\\mathbf{y}\\right) \\mathbf{u}_{1}+\\left(\\mathbf{u}_{2}^T\\mathbf{y}\\right) \\mathbf{u}_{2}+\\cdots+\\left(\\mathbf{u}_{p}^T\\mathbf{y}\\right) \\mathbf{u}_{p}\\\\\n",
    "\\end{align}"
   ]
  }
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