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
  $$\begin{array}{c}PA=\left[\begin{array}{ccc}1& 0& 0\\ & & \\ 0& 0& 1\\ & & \\ 0& 1& 0\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ & & \\ 4& 5& 6\\ & & \\ 7& 8& 9\end{array}\right]=\left[\begin{array}{ccc}1& 2& 3\\ & & \\ 7& 8& 9\\ & & \\ 4& 5& 6\end{array}\right]\end{array}$$

2. numpy.dot

• numpy.dot(A,P)–> AP 列变换

import numpy as np

if __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}")