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ddeguchi committed Dec 19, 2018
1 parent 9de6e5c commit b08f32bb21f49ab440b08a407c51cacb1484d8a9
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\documentclass{article}
\usepackage{epsfig}
\pagestyle{empty}
\begin{document}
\[ \mbox{\boldmath p} = \mbox{\boldmath q} \rightarrow p_r = q_r \; \wedge \; p_g = q_g \; \wedge \; p_b = q_b \]
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\[ \mbox{\boldmath p} \neq \mbox{\boldmath q} \rightarrow \overline{ p_r = q_r \; \wedge \; p_g = q_g \; \wedge \; p_b = q_b } \]
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\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow \overline{ p_r \ge q_r \; \wedge \; p_g \ge q_g \; \wedge \; p_b \ge q_b } \]
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\[ \mbox{\boldmath p} \le \mbox{\boldmath q} \rightarrow p_r \le q_r \; \wedge \; p_g \le q_g \; \wedge \; p_b \le q_b \]
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\[ \mbox{\boldmath p} \le \mbox{\boldmath q} \rightarrow \overline{ p_r \le q_r \; \wedge \; p_g \le q_g \; \wedge \; p_b \le q_b } \]
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\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow p_r \ge q_r \; \wedge \; p_g \ge q_g \; \wedge \; p_b \ge q_b \]
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$ a = b $
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$ a \neq b $
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$ a \subset b $
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$ a \subseteq b $
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$ a \supset b $
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$ a \supseteq b $
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\[ a = a \bigcup b \]
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\[ a = a - \left( a \bigcap b \right) \]
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\[ a = a \bigcap b \]
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\[ \mbox{\boldmath p} = \mbox{\boldmath q} \rightarrow p_l = q_l \; \wedge \; p_r = q_r \]
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\[ \mbox{\boldmath p} \neq \mbox{\boldmath q} \rightarrow \overline{ p_l = q_l \; \wedge \; p_r = q_r } \]
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\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow \overline{ p_l \ge q_l \; \wedge \; p_r \ge q_r } \]
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\[ \mbox{\boldmath p} \le \mbox{\boldmath q} \rightarrow p_l \le q_l \; \wedge \; p_r \le q_r \]
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\[ \mbox{\boldmath p} \le \mbox{\boldmath q} \rightarrow \overline{ p_l \le q_l \; \wedge \; p_r \le q_r } \]
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\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow p_l \ge q_l \; \wedge \; p_r \ge q_r \]
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$l^2$
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$a_x$
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$l a_x$
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\[ \left( \begin{array}{ccc} \sigma_1 & 0 & 0 \\ 0 & \sigma_2 & 0 \\ 0 & 0 & \sigma_3 \end{array} \right) \]
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$ \sigma_1 \ge \sigma_2 \ge \sigma_3 $
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\[ {\bf A} = {\bf A} + {\bf B} \]
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\[ {\bf A} = {\bf A} - {\bf B} \]
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\[ {\bf A} = {\bf A} * {\bf B} \]
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\[ {\bf A} = {\bf A} + val * {\bf I} \]
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\[ {\bf A} = {\bf A} - val * {\bf I} \]
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\[ {\bf A} = {\bf A} * val \]
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\[ {\bf A} = {\bf A} / val \]
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$ a \ge b \ge c $
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$ c \ge b \ge a $
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$ f(a) $
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$ f(b) $
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$ f(c) $
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$\displaystyle-\min_{i} \left\{ -H_{ii} \right\}$
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$\displaystyle\max_{i} \left\{ -H_{ii} + \sum_{i \ne j}{\|H_{ij}\|} \right\}$
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\[ {\bf C} = \alpha \times {\bf A} \times {\bf B} + \beta \times {\bf C} \]
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${\bf A}$
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${\bf B}$
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${\bf C}$
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\[ {\bf C} = {\bf A} \times {\bf B} \]
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\[ tr\left( {\bf A} \right) = \sum^{n}_{i=1}{ a_{ii} } \]
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$tr\left( {\bf A} \right)$
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\[ \left| {\bf A} \right| = \left| \begin{array}{ccccc} a_{11} & \cdots & a_{1j} & \cdots & a_{1n} \\ a_{21} & \cdots & a_{2j} & \cdots & a_{2n} \\ \vdots & \cdots & \vdots & \cdots & \vdots \\ a_{n1} & \cdots & a_{nj} & \cdots & a_{nn} \end{array} \right| = \sum^{n}_{j=1}{ \left( -1 \right)^{j+1} a_{1j} \left| \begin{array}{cccccc} a_{21} & \cdots & a_{2,j-1} & a_{2,j+1} & \cdots & a_{2n} \\ \vdots & \cdots & \vdots & \vdots & \cdots & \vdots \\ a_{n1} & \cdots & a_{n,j-1} & a_{n,j+1} & \cdots & a_{nn} \end{array} \right| } \]
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$\left| {\bf A} \right|$
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\[ {\bf A}\mbox{\boldmath x} = \mbox{\boldmath b} \]
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$\mbox{\boldmath b}$
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$\mbox{\boldmath x}$
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\[ {\bf A} = {\bf P} \; \times \; {\bf L} \; \times \; {\bf U} \]
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$\mbox{\bf A}$
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$\mbox{\bf L}$
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$\mbox{\bf U}$
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$\mbox{\bf P}$
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\[ {\bf A} = {\bf Q} \; {\bf R} \]
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\[ {\bf A}^{-1} \]
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$ {\bf A}^{-1} $
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\[ {\bf A}\mbox{\boldmath x} = \lambda\mbox{\boldmath x} \]
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$\lambda$
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\[ {\bf A} = {\bf U}{\bf \Sigma}{\bf V}^T \]
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$ {\bf A} $
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$ {\bf U} $
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$ {\bf \Sigma} $
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$ {\bf V}^T $
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\[ \mbox{\boldmath p} + \mbox{\boldmath q} = \left( p_w + q_w \;,\; p_x + q_x \;,\; p_y + q_y \;,\; p_z + q_z \right)^T \]
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\[ \mbox{\boldmath p} + a = \left( p_w + a \;,\; p_x \;,\; p_y \;,\; p_z \right)^T \]
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\[ \mbox{\boldmath p} - \mbox{\boldmath q} = \left( p_w - q_w \;,\; p_x - q_x \;,\; p_y - q_y \;,\; p_z - q_z \right)^T \]
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\[ \mbox{\boldmath p} - a = \left( p_w - a \;,\; p_x \;,\; p_y \;,\; p_z \right)^T \]
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\[ \mbox{\boldmath p} \times \mbox{\boldmath q} = \left( p_w \times q_w - p_x \times q_x - p_y \times q_y - p_z \times q_z \;,\; p_w \times q_x + p_x \times q_w + p_y \times q_z - p_z \times q_y \;,\; p_w \times q_y + p_y \times q_w + p_z \times q_x - p_x \times q_z \;,\; p_w \times q_z + p_z \times q_w + p_x \times q_y - p_y \times q_x \right)^T \]
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\[ \mbox{\boldmath p} \times a = \left( p_w \times a \;,\; p_x \times a \;,\; p_y \times a \;,\; p_z \times a \right)^T \]
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\[ \frac{ \mbox{\boldmath p} }{ \mbox{\boldmath q} } = \mbox{\boldmath p} \times \mbox{\boldmath q}^{-1} \]
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\[ \mbox{\boldmath p} \div a = \left( p_w \div a \;,\; p_x \div a \;,\; p_y \div a \;,\; p_z \div a \right)^T \]
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\[ \mbox{\boldmath p} == \mbox{\boldmath q} \rightarrow p_w == q_w \; \wedge \; p_x == q_x \; \wedge \; p_y == q_y \; \wedge \; p_z == q_z \]
\pagebreak

\[ \mbox{\boldmath p} \neq \mbox{\boldmath q} \rightarrow \overline{ p_w = q_w \; \wedge \; p_x = q_x \; \wedge \; p_y = q_y \; \wedge \; p_z = q_z } \]
\pagebreak

\[ \mbox{\boldmath p} < \mbox{\boldmath q} \rightarrow \overline{ p_w \ge q_w \; \wedge \; p_x \ge q_x \; \wedge \; p_y \ge q_y \; \wedge \; p_z \ge q_z } \]
\pagebreak

\[ \mbox{\boldmath p} \le \mbox{\boldmath q} \rightarrow p_w \le q_w \; \wedge \; p_x \le q_x \; \wedge \; p_y \le q_y \; \wedge \; p_z \le q_z \]
\pagebreak

\[ \mbox{\boldmath p} > \mbox{\boldmath q} \rightarrow \overline{ p_w \le q_w \; \wedge \; p_x \le q_x \; \wedge \; p_y \le q_y \; \wedge \; p_z \le q_z } \]
\pagebreak

\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow p_w \ge q_w \; \wedge \; p_x \ge q_x \; \wedge \; p_y \ge q_y \; \wedge \; p_z \ge q_z \]
\pagebreak

\[ \overline{ \mbox{\boldmath p} } = \left( p_w \;,\; -p_x \;,\; -p_y \;,\; -p_z \right)^T \]
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\[ \mbox{\boldmath p}^{-1} = \frac{ \overline{ \mbox{\boldmath p} } }{ \left\| \mbox{\boldmath p} \right\|^2 } \]
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\[ \frac{ \mbox{\boldmath p} }{ \left\| \mbox{\boldmath p} \right\|^2 } \]
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\[ p_w \times q_w + p_x \times q_x + p_y \times q_y + p_z \times q_z \]
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\[ \left\| \mbox{\boldmath p} \right\| = \sqrt{ p_w^2 + p_x^2 + p_y^2 + p_z^2 } \]
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\[ \mbox{\boldmath p} = \mbox{\boldmath q} \rightarrow p_x = q_x \; \wedge \; p_y = q_y \; \wedge \; p_z = q_z \]
\pagebreak

\[ \mbox{\boldmath p} \neq \mbox{\boldmath q} \rightarrow \overline{ p_x = q_x \; \wedge \; p_y = q_y \; \wedge \; p_z = q_z} \]
\pagebreak

\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow \overline{ p_x \ge q_x \; \wedge \; p_y \ge q_y \; \wedge \; p_z \ge q_z } \]
\pagebreak

\[ \mbox{\boldmath p} \le \mbox{\boldmath q} \rightarrow p_x \le q_x \; \wedge \; p_y \le q_y \; \wedge \; p_z \le q_z \]
\pagebreak

\[ \mbox{\boldmath p} \le \mbox{\boldmath q} \rightarrow \overline{ p_x \le q_x \; \wedge \; p_y \le q_y \; \wedge \; p_z \le q_z } \]
\pagebreak

\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow p_x \ge q_x \; \wedge \; p_y \ge q_y \; \wedge \; p_z \ge q_z \]
\pagebreak

\[ \frac{\mbox{\boldmath v}}{\left\|{\mbox{\boldmath v}}\right\|} \]
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\[ \mbox{\boldmath p} \cdot \mbox{\boldmath q} = p_x \times q_x + p_y \times q_y + p_z \times q_z \]
\pagebreak

\[ \mbox{\boldmath p} \times \mbox{\boldmath q} = \left( p_y \times q_z - p_z \times q_y \;,\; p_z \times q_x - p_x \times q_z \;,\; p_x \times q_y - p_y \times q_x \right)^T \]
\pagebreak

\[ \left\|\mbox{\boldmath v}\right\| = \sqrt{v_x^2 + v_y^2 + v_z^2} \]
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\[ \mbox{\boldmath p} = \mbox{\boldmath q} \rightarrow p_x = q_x \; \wedge \; p_y = q_y \]
\pagebreak

\[ \mbox{\boldmath p} \neq \mbox{\boldmath q} \rightarrow \overline{ p_x = q_x \; \wedge \; p_y = q_y } \]
\pagebreak

\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow \overline{ p_x \ge q_x \; \wedge \; p_y \ge q_y } \]
\pagebreak

\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow p_x \le q_x \; \wedge \; p_y \le q_y \]
\pagebreak

\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow \overline{ p_x \le q_x \; \wedge \; p_y \le q_y } \]
\pagebreak

\[ \mbox{\boldmath p} \ge \mbox{\boldmath q} \rightarrow p_x \ge q_x \; \wedge \; p_y \ge q_y \]
\pagebreak

\[ \frac{\mbox{\boldmath v}}{\left\|\mbox{\boldmath v}\right\|} \]
\pagebreak

\[ \mbox{\boldmath p} \cdot \mbox{\boldmath q} = p_x \times q_x + p_y \times q_y \]
\pagebreak

\[ \mbox{\boldmath p} \times \mbox{\boldmath q} = p_x \times q_y - p_y \times q_x \]
\pagebreak

\[ \left\|\mbox{\boldmath v}\right\| = \sqrt{v_x^2+v_y^2} \]
\pagebreak

\end{document}
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