1. 左行右列

假设有两个矩阵A,P 对于矩阵A来说，

• AP矩阵中，P在A的右边，那么对于矩阵A来说是对矩阵A进行列变换
• PA矩阵中，P在A的左边，那么对于矩阵A来说是对矩阵A进行行变换
  $$\begin{array}{c}A=\left[\begin{array}{ccc}1& 2& 3\\ & & \\ 4& 5& 6\\ & & \\ 7& 8& 9\end{array}\right];P=\left[\begin{array}{ccc}1& 0& 0\\ & & \\ 0& 0& 1\\ & & \\ 0& 1& 0\end{array}\right];\end{array}$$
• AP,将第二列和第三列互换
  $$\begin{array}{c}AP=\left[\begin{array}{ccc}1& 2& 3\\ & & \\ 4& 5& 6\\ & & \\ 7& 8& 9\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ & & \\ 0& 0& 1\\ & & \\ 0& 1& 0\end{array}\right]=\left[\begin{array}{ccc}1& 3& 2\\ & & \\ 4& 6& 5\\ & & \\ 7& 9& 8\end{array}\right];\end{array}$$
• PA,将第二行和第三行互换
  $$\begin{array}{c}PA=\left[\begin{array}{ccc}1& 0& 0\\ & & \\ 0& 0& 1\\ & & \\ 0& 1& 0\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ & & \\ 4& 5& 6\\ & & \\ 7& 8& 9\end{array}\right]=\left[\begin{array}{ccc}1& 2& 3\\ & & \\ 7& 8& 9\\ & & \\ 4& 5& 6\end{array}\right]\end{array}$$

numpydot_41">2. numpy.dot

• numpy.dot(A,P)–> AP 列变换

import numpy as npif __name__ == "__main__":A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])# A=[[1 2 3]# [4 5 6]# [7 8 9]]P = np.array([[1, 0, 0], [0, 0, 1], [0, 1, 0]])# P=[[1 0 0]# [0 0 1]# [0 1 0]]# AP 列变换column_permutation = np.dot(A, P)# column_permutation=# [[1 3 2]# [4 6 5]# [7 9 8]]# PA 行变换row_permutation = np.dot(P, A)# row_permutation=# [[1 2 3]# [7 8 9]# [4 5 6]]print(f"A={A}")print(f"P={P}")print(f"column_permutation=\n{column_permutation}")print(f"row_permutation=\n{row_permutation}")