Invert A Matrix

h1ros

Goal¶

This post aims to show how to invert a matrix using numpy i.e., calculating a inverse matrix $A^{-1}$ from $A$

For example, if we have

$$A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} $$

Then, $A^{-1}$ should meet with

$$A A^{-1} = I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$

Reference:

In [1]:

import numpy as np
from numpy.linalg import inv

In [2]:

arr = np.array([[1, 2], [3, 4]])
arr

Out[2]:

array([[1, 2],
       [3, 4]])

In [3]:

arr_inv = inv(arr)
arr_inv

Out[3]:

array([[-2. ,  1. ],
       [ 1.5, -0.5]])

In [4]:

np.dot(arr_inv, arr)

Out[4]:

array([[1.00000000e+00, 0.00000000e+00],
       [2.22044605e-16, 1.00000000e+00]])

In [5]:

np.dot(arr, arr_inv)

Out[5]:

array([[1.0000000e+00, 0.0000000e+00],
       [8.8817842e-16, 1.0000000e+00]])