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The inverse of a matrix is just a reciprocal of the matrix as we do in normal arithmetic for a single number which is used to solve the equations to find the value of unknown variables. The inverse of a matrix is that matrix which when multiplied with the original matrix will give as an identity matrix. The inverse of a matrix exists only if the matrix is non-singular i.e., determinant should not be 0. Using determinant and adjoint, we can easily find the inverse of a square matrix using below formula,
if det[A] != 0
A-1 = adj[A]/det[A]
else
"Inverse doesn't exist" Matrix Equation
where,
A-1: The inverse of matrix A
x: The unknown variable column
B: The solution matrix
Inverse of a Matrix using NumPy
Python provides a very easy method to calculate the inverse of a matrix. The function numpy.linalg.inv[] which is available in the python NumPy module is used to compute the inverse of a matrix.
Syntax:
numpy.linalg.inv[a]
Parameters:
a: Matrix to be inverted
Returns:
Inverse of the matrix a.
Example 1:
Python
import numpy as np
A = np.array[[[6, 1, 1],
[4, -2, 5],
[2, 8, 7]]]
print[np.linalg.inv[A]]
Output:
[[ 0.17647059 -0.00326797 -0.02287582] [ 0.05882353 -0.13071895 0.08496732] [-0.11764706 0.1503268 0.05228758]]
Example 2:
Python
import numpy as np
A = np.array[[[6, 1, 1, 3],
[4, -2, 5, 1],
[2, 8, 7, 6],
[3, 1, 9, 7]]]
print[np.linalg.inv[A]]
Output:
[[ 0.13368984 0.10695187 0.02139037 -0.09090909] [-0.00229183 0.02673797 0.14820474 -0.12987013] [-0.12987013 0.18181818 0.06493506 -0.02597403] [ 0.11000764 -0.28342246 -0.11382735 0.23376623]]
Example 3:
Python
import numpy as np
A = np.array[[[[1., 2.], [3., 4.]],
[[1, 3], [3, 5]]]]
print[np.linalg.inv[A]]
Output:
[[[-2. 1. ] [ 1.5 -0.5 ]] [[-1.25 0.75] [ 0.75 -0.25]]]