Lecture 1 Introduction¶
Review of Linear Algrebra¶
Affine Transformations 仿射变换¶
Affine map combines linear map and translation.
\[
\begin{bmatrix}
x' \\
y'
\end{bmatrix}
=
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
+
\begin{bmatrix}
t_x \\
t_y
\end{bmatrix} .
\]
Using homogenous coordinates (齐次坐标)
\[
\begin{bmatrix}
x' \\
y' \\
1
\end{bmatrix}
=
\begin{bmatrix}
a & b & t_x \\
c & d & t_y \\
0 & 0 & 1
\end{bmatrix}
\begin{bmatrix}
x \\
y \\
1
\end{bmatrix}.
\]
Eigenvectors and Eigenvalues¶
- The eigenvalues of symmetric matrices are real numbers.
- The eigenvalues of positive definite matrices are positive numbers.
最后更新:
2023.01.16 00:06:03 CST
创建日期: 2022.11.08 20:35:08 CST
创建日期: 2022.11.08 20:35:08 CST