NumPy: Inverse Matrix

In Python, the inverse of a matrix can be calculated importing NumPy linalg.

import numpy as np
from numpy import linalg

A = np.array([[-2, 5], [3, 1]])
B = linalg.inv(A)

print(B)
'''
[[-0.05882353  0.29411765]
 [ 0.17647059  0.11764706]]
'''

linalg is often used for vector/matrix calculations and linalg.inv returns the inverse matrix.

LinAlgError

All matrices don't always have the inverse matrices and inv raises the exception if the matrix doesn't have the inverse.

import numpy as np
from numpy import linalg

A = np.array([[2, 1], [2, 1]])
B = linalg.inv(A)

# numpy.linalg.LinAlgError: Singular matrix

\[ det(A) = 0 \]

so A doesn't have an inverse matrix. NumPy is so smart that it calculates the determinant of a matrix exactly.

import numpy as np
from numpy import linalg

A = np.array([[2, 0.5], [4, 1]])
B = linalg.inv(A)

# numpy.linalg.LinAlgError: Singular matrix

The same is true of fractions.

import numpy as np
from numpy import linalg

A = np.array([[2, 1 / 2], [4, 1]])
B = linalg.inv(A)

# numpy.linalg.LinAlgError: Singular matrix

Dimension error

In algebra, the inverse of a square matrix can not be defined.

import numpy

from numpy import linalg

A = numpy.array([[1, 2, 3], [4, 5, 6]])

B = linalg.inv(A)

print(B)
# numpy.linalg.LinAlgError: Last 2 dimensions of the array must be square

Note: NumPy shape returns the dimension (shape) of a matrix. The shape of A is (2, 3).