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np.linalg.inv: How to Inverse Matrix in Python

In mathematics, the inverse of a matrix is the reciprocal of a number. The Inverse of a Matrix is identical, but we write it A^-1. When we multiply a number by its reciprocal, we get 1.

Why do we need an Inverse?

We need an inverse of the Matrix because matrices we don’t divide! Thoughtfully, there is no concept of dividing by a matrix. But we can multiply by an inverse to achieve the same thing. So let’s see how to inverse the numpy Matrix in Python.

np.linalg.inv

The np.linalg.inv() is a numpy library function that computes a matrix’s (multiplicative) inverse. The inverse of a matrix is a reciprocal of a matrix.

To find the inverse of the Matrix in Python, use the np.linalg.inv() method. It is also defined as a matrix formed that gives an identity matrix when multiplied with the original Matrix.

A matrix’s inverse occurs only if it is a non-singular matrix, i.e., the determinant of a matrix should be 0.

Equation For Getting Inverse Of A Matrix

A*x= B
A^-1 A*x= A-1 B
x= A-1 B

Where A^-1: It denotes the inverse of a matrix.

                x: It denotes an unknown column.

                B: It denotes the solution matrix.

Now, let’s see the procedure for using Numpy to find the inverse of a matrix.

Syntax

numpy.linalg.inv(A)

Parameters

A: It denotes the Matrix to be inverted.

Return Value

The inverse of Matrix A is returned.

Note

The inv() function raises a LinAlgError if A is not a square matrix because if A is not a square matrix, inversion fails.

Example

Inversion of 4*4 Matrix.

import numpy as np

A = np.array([[-5, -2, 3, 4],
              [3, 1, 2, 7],
              [2, 7, -5, 2],
              [6, -6, 8, 4]])

print(np.linalg.inv(A))

Output

[[-0.19186047  0.1627907  -0.11046512 -0.0377907 ]
 [ 0.64534884 -1.09302326  1.09883721  0.71802326]
 [ 0.73837209 -1.23255814  1.12209302  0.85755814]
 [-0.22093023  0.58139535 -0.43023256 -0.33139535]]

Explanation

Here A matrix was given as input to the function, and after that Inverse of a matrix was returned as the output.

Calculating inverses of several matrices

import numpy as np

A = np.array([[[3., 4.], [4., 5.]],
              [[6, 7], [7, 9]]])

print(np.linalg.inv(A))

Output

[[[-5.   4. ]
  [ 4.  -3. ]]

 [[ 1.8 -1.4]
  [-1.4  1.2]]]

Explanation

Here, we have given several matrices as an input to the function, and after that inverse of a matrix was returned as the output.

That is it for Numpy.linalg.inv() function.

See also

Numpy linalg lstsq()

Numpy linalg slogdet()

Numpy linalg solve()

Numpy linalg svd()

Numpy linalg qr()

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