mvg:lecture_01:start
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mvg:lecture_01:start [2018/11/19 09:32] – [Group] admin | mvg:lecture_01:start [2018/11/19 09:55] (current) – [Group] admin | ||
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Set of invertible square matrices form the General Linear Group GL(n). They are closed with respect to multiplication. | Set of invertible square matrices form the General Linear Group GL(n). They are closed with respect to multiplication. | ||
- | $\det(R) = 1$ | + | $\det(M) = 1$ |
$R: G \rightarrow GL(n)$ | $R: G \rightarrow GL(n)$ | ||
Line 140: | Line 140: | ||
$R$ is a group **homomorphism**. | $R$ is a group **homomorphism**. | ||
+ | === Affine Group $A(n)$ === | ||
+ | |||
+ | $L(x) = A(x) + b$ | ||
+ | |||
+ | $L: \mathbb{R}^{n+1}\rightarrow \mathbb{R}^{n+1}$ | ||
+ | |||
+ | $\left( \begin{array}{cc} | ||
+ | A & \mathbf{x} | ||
+ | 0 & 1 \\\\ | ||
+ | \end{array}\right) $ | ||
+ | |||
+ | |||
+ | ===== Appendix: My MathJax Template for a Matrix ===== | ||
+ | |||
+ | $\left( \begin{array}{rrrr} | ||
+ | 1 & 0 & \cdots & 0 \\\\ | ||
+ | 0 & \ddots & 0 & \vdots \\\\ | ||
+ | \vdots & 0 & \ddots & 0 \\\\ | ||
+ | 0 & \cdots & 0 & 1 | ||
+ | \end{array}\right) $ | ||
mvg/lecture_01/start.1542619966.txt.gz · Last modified: 2018/11/19 09:32 by admin