线性代数矩阵乘积的逆_矩阵的乘积及其逆性质 使用Python的线性代数

线性代数矩阵乘积的逆

Prerequisites:

先决条件：

• Defining a Matrix

  定义矩阵

• Inverse of a Matrix

  矩阵的逆

In linear algebra, an nxn square matrix A can be called as invertible if its inverse exists. Notice that, there cannot be a non-square matrix whose inverse exists. In this tutorial, we are going to check and verify one of the properties of Invertible Matrices.

在线性代数中，如果存在一个nxn方阵A的逆，则它可以称为可逆的。 注意，不能存在一个存在逆函数的非方阵。 在本教程中，我们将检查和验证可逆矩阵的属性之一。

^-.1 = I^-.1 = I

用于查找矩阵乘积及其逆属性的Python代码 (Python code to find the product of a matrix and its inverse property)

# Linear Algebra Learning Sequence
# Inverse Property A.AI = I  [AI = inverse of A]

import numpy as np

M = np.array([[2,3,4], [4,4,8], [4,8,7]])
print("---Matrix A---\n", M)

MI = np.linalg.inv(M) 
print('\n\nInverse of A (AI) as ----\n', MI)

pro = np.dot(MI,M)
print('\n\nProduct of Matrix A with its Inverse : A * AI = I \n\n', pro)

Output:

输出：

---Matrix A---
 [[2 3 4]
 [4 4 8]
 [4 8 7]]


Inverse of A (AI) as ----
 [[-9.    2.75  2.  ]
 [ 1.   -0.5   0.  ]
 [ 4.   -1.   -1.  ]]


Product of Matrix A with its Inverse : A * AI = I 

 [[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

翻译自: https://www.includehelp.com/python/product-of-a-matrix-and-its-inverse-property.aspx

线性代数矩阵乘积的逆