Inverse and Transpose Matrix in Numpy

• Numpy Import
• Initialize Matrix A
• Transpose A
• Inverse A
• What is A^(-1)*A?
• Become Identity Matrix is it? can see by below
• Now what happens when we multiply A * A_invA = A itself ?

Numpy Import

import numpy as np

Initialize Matrix A

A_np = np.array([[1,2,0],[0,5,6],[7,0,9]])
A_np

array([[1, 2, 0],
       [0, 5, 6],
       [7, 0, 9]])

Transpose A

A_trans = A_np.transpose()
A_trans

array([[1, 0, 7],
       [2, 5, 0],
       [0, 6, 9]])

Inverse A

A_inv = np.linalg.inv(A_np)
A_inv

array([[ 0.34883721, -0.13953488,  0.09302326],
       [ 0.3255814 ,  0.06976744, -0.04651163],
       [-0.27131783,  0.10852713,  0.03875969]])

What is A^(-1)*A?

A_invA = np.linalg.inv(A_np) @ A_np
A_invA

array([[ 1.00000000e+00,  0.00000000e+00,  1.80411242e-16],
       [ 2.08166817e-17,  1.00000000e+00,  3.46944695e-17],
       [-3.46944695e-17,  0.00000000e+00,  1.00000000e+00]])

Become Identity Matrix is it? can see by below

Now what happens when we multiply A * A_invA = A itself ?

AI = A_np @ A_invA
AI

array([[ 1.00000000e+00,  2.00000000e+00,  2.49800181e-16],
       [-1.04083409e-16,  5.00000000e+00,  6.00000000e+00],
       [ 7.00000000e+00,  0.00000000e+00,  9.00000000e+00]])