How to Fix Inverse of Matrix in Python

1. Use the numpy.linalg.inv() Function to Find the Inverse of a Matrix in Python
2. Use the numpy.matrix Class to Find the Inverse of a Matrix in Python
3. Use the scipy.linalg.inv() Function to Find the Inverse of a Matrix in Python
4. Create a User-Defined Function to Find the Inverse of a Matrix in Python

A matrix is a two-dimensional array with every element of the same size. We can represent matrices using numpy arrays or nested lists.

For a non-singular matrix whose determinant is not zero, there is a unique matrix that yields an identity matrix when multiplied with the original. This unique matrix is called the inverse of the original matrix.

This tutorial will demonstrate how to inverse a matrix in Python using several methods.

Use the numpy.linalg.inv() Function to Find the Inverse of a Matrix in Python

The numpy module has different functionalities to create and manipulate arrays in Python. The numpy.linalg submodule implements different linear algebra algorithms and functions.

We can use the numpy.linalg.inv() function from this module to compute the inverse of a given matrix. This function raises an error if the inverse of a matrix is not possible, which can be because the matrix is singular.

Therefore, using this function in a try and except block is recommended. If the matrix is singular, an error will be raised, and the code in the except block will be executed.

Code Snippet:

import numpy as np

try:
    m = np.array([[4, 3], [8, 5]])
    print(np.linalg.inv(m))
except:
    print("Singular Matrix, Inverse not possible.")

Output:

[[-1.25  0.75]
 [ 2.   -1.  ]]

Use the numpy.matrix Class to Find the Inverse of a Matrix in Python

For a long time, the numpy.matrix class was used to represent matrices in Python. This is the same as using a normal two-dimensional array for matrix representation.

A numpy.matrix object has the attribute numpy.matrix.I computed the inverse of the given matrix. It also raises an error if a singular matrix is used.

Code Snippet:

import numpy as np

try:
    m = np.matrix([[4, 3], [8, 5]])
    print(m.I)
except:
    print("Singular Matrix, Inverse not possible.")

Output:

[[-1.25  0.75]
 [ 2.   -1.  ]]

Although both the methods work the same internally, using the numpy.matrix class is discouraged. This is because it has been deprecated and ambiguous while working with numpy arrays.

Use the scipy.linalg.inv() Function to Find the Inverse of a Matrix in Python

We can use the scipy module to perform different scientific calculations using its functionalities. It works well with numpy arrays as well.

The scipy.linalg.inv() can also return the inverse of a given square matrix in Python. It works the same way as the numpy.linalg.inv() function.

Code Snippet:

import numpy as np
from scipy import linalg

try:
    m = np.matrix([[4, 3], [8, 5]])
    print(linalg.inv(m))
except:
    print("Singular Matrix, Inverse not possible.")

Output:

[[-1.25  0.75]
 [ 2.   -1.  ]]

Create a User-Defined Function to Find the Inverse of a Matrix in Python

We can implement the mathematical logic for calculating an inverse matrix in Python. For this, we will use a series of user-defined functions.

We will create different functions to return the determinants, transpose, and matrix determinants. These functions will be used in a function that will return the final inverse.

This method works when we represent a matrix as a list of lists in Python.

Code Snippet:

def return_transpose(mat):
    return map(list, zip(*mat))


def return_matrix_minor(mat, i, j):
    return [row[:j] + row[j + 1 :] for row in (mat[:i] + mat[i + 1 :])]


def return_determinant(mat):
    if len(mat) == 2:
        return mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0]

    determinant = 0
    for c in range(len(m)):
        determinant += (
            ((-1) ** c) * m[0][c] * return_determinant(return_matrix_minor(m, 0, c))
        )
    return determinant


def inverse_matrix(m):
    determinant = return_determinant(m)
    if len(m) == 2:
        return [
            [m[1][1] / determinant, -1 * m[0][1] / determinant],
            [-1 * m[1][0] / determinant, m[0][0] / determinant],
        ]

    cfs = []
    for r in range(len(m)):
        cfRow = []
        for c in range(len(m)):
            minor = return_matrix_minor(m, r, c)
            cfRow.append(((-1) ** (r + c)) * return_determinant(minor))
        cfs.append(cfRow)
    cfs = return_transpose(cfs)
    for r in range(len(cfs)):
        for c in range(len(cfs)):
            cfs[r][c] = cfs[r][c] / determinant
    return cfs


m = [[4, 3], [8, 5]]
print(inverse_matrix(m))

Output:

[[-1.25, 0.75], [2.0, -1.0]]

The above example returns a nested list that represents the given matrix’s inverse.

To wrap up, we discussed several methods to find the inverse of a matrix in Python. The numpy and scipy modules have the linalg.inv() function that computes the inverse of a matrix.

We can also use the numpy.matrix class to find the inverse of a matrix. Finally, we discussed a series of user-defined functions that compute the inverse by implementing the arithmetical logic.