lectures:一次変換
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lectures:一次変換 [2019/05/23 22:24] – kimi | lectures:一次変換 [2019/05/23 23:46] – [証明] kimi | ||
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====== 一次変換 ====== | ====== 一次変換 ====== | ||
- | $\vec{x}\in R$\mathbb{R}$ | + | ===== 定義 ===== |
+ | $$ | ||
+ | \left\{ | ||
+ | \begin{array}{ll} | ||
+ | | ||
+ | \vec{x} \in \mathbb{R}^n, k \in \mathbb{R}^1, | ||
+ | \end{array} | ||
+ | \right. \Leftrightarrow f(\vec{x})=A\vec{x} | ||
+ | $$ | ||
+ | ==== 証明 ==== | ||
+ | |||
+ | $$\vec{y}=f(\vec{x})$$ | ||
+ | |||
+ | $$\vec{x}=x_1\vec{e}_1+x_2\vec{e}_2+\cdots$$ | ||
+ | |||
+ | $$\vec{y}=y_1\vec{e}_1+y_2\vec{e}_2+\cdots$$ | ||
+ | |||
+ | $$ | ||
+ | \begin{array}{rcl} | ||
+ | f(\vec{x})& | ||
+ | & | ||
+ | & | ||
+ | \end{array} | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | \begin{array}{rcl} | ||
+ | f(\vec{e}_1)& | ||
+ | f(\vec{e}_2)& | ||
+ | & | ||
+ | \end{array} | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | \begin{array}{rcl} | ||
+ | f(\vec{x})& | ||
+ | & | ||
+ | & & | ||
+ | & & | ||
+ | & | ||
+ | & & | ||
+ | & & | ||
+ | \end{array} | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | \begin{array}{rcl} | ||
+ | y_1\vec{e}_1+y_2\vec{e}_2+\cdots & | ||
+ | & & | ||
+ | & & | ||
+ | \end{array} | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | \left\{\begin{array}{rcl} | ||
+ | y_1& | ||
+ | y_2& | ||
+ | & | ||
+ | \end{array} | ||
+ | \right. | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | \left[\begin{array}{c} | ||
+ | y_1\\ | ||
+ | y_2\\ | ||
+ | \ldots\\ | ||
+ | \end{array} | ||
+ | \right] | ||
+ | =\left[\begin{array}{ccc} | ||
+ | a_{11}& | ||
+ | a_{21}& | ||
+ | \ldots & & \\ | ||
+ | \end{array} | ||
+ | \right] | ||
+ | \left[\begin{array}{c} | ||
+ | x_{1}\\ | ||
+ | x_{2}\\ | ||
+ | \ldots\\ | ||
+ | \end{array} | ||
+ | \right] | ||
+ | $$ |
lectures/一次変換.txt · 最終更新: 2022/08/23 13:34 by 127.0.0.1