Matrix Inverse

Inverting a matrix is a process of finding a matrix such that, if multiplied by the original matrix, the result is an Identity matrix. Mathematically, inversion is represented as:

$A^{-1}$ is an inverse matrics of $A$ if $$A*A^{-1}=I$$

It is important to note that not all matrices are invertible.

Implementation in Numpy

The method linalg.inv returns the inverse of a given matrix.

import numpy as np

A = np.array([ 2, 3, 4, 3]).reshape(2,2)
np.linalg.inv(A)

array([[-0.5 , 0.5 ], [ 0.66666667, -0.33333333]])

Confirm that the dot product of the inverse and original matrix is an identity matrix

A.dot(np.linalg.inv(A))

array([[1., 0.], [0., 1.]])