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--- mvg:lecture_01:start [2018/11/19 09:25] – [Group] admin
+++ mvg:lecture_01:start [2018/11/19 09:55] (current) – [Group] admin
@@ Line 130: / Line 130: @@
 Set of invertible square matrices form the General Linear Group GL(n). They are closed with respect to multiplication.
+$\det(M) = 1$
+$R: G \rightarrow GL(n)$
+$R(e) = I, R(g\circ h) = R(g)R(h), \all g,h \in G$
-$\det(M) = 1$
+"It preserves the group structure!" (DC)
+$R$ 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}  \\\\
+& 1 \\\\
+\end{array}\right) $
+===== Appendix: My MathJax Template for a Matrix =====
+$\left( \begin{array}{rrrr}
+& 0 & \cdots & 0 \\\\
+& \ddots & 0 & \vdots \\\\
+\vdots & 0 & \ddots & 0 \\\\
+& \cdots & 0 & 1
+\end{array}\right) $