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
We can find out the inverse of any square matrix with the function numpy.linalg.inv(array).
Syntax: numpy.linalg.inv(a)
Parameters:
a: Matrix to be inverted
Returns: Inverse of the matrix a.
Example 1:
Python3
# Importing Library import numpy as np # Finding an inverse of given array arr = np.array([[1, 2], [5, 6]]) inverse_array = np.linalg.inv(arr) print("Inverse array is ") print(inverse_array) print() # inverse of 3X3 matrix arr = np.array([[1, 2, 3], [4, 9, 6], [7, 8, 9]]) inverse_array = np.linalg.inv(arr) print("Inverse array is ") print(inverse_array) print() # inverse of 4X4 matrix arr = np.array([[1, 2, 3, 4], [10, 11, 14, 25], [20, 8, 7, 55], [40, 41, 42, 43]]) inverse_array = np.linalg.inv(arr) print("Inverse array is ") print(inverse_array) print() # inverse of 1X1 matrix arr = np.array([[1]]) inverse_array = np.linalg.inv(arr) print("Inverse array is ") print(inverse_array) |
Output:
Inverse array is [[-1.5 0.5 ] [ 1.25 -0.25]] Inverse array is [[-0.6875 -0.125 0.3125 ] [-0.125 0.25 -0.125 ] [ 0.64583333 -0.125 -0.02083333]] Inverse array is [[-15.07692308 4.9 -0.8 -0.42307692] [ 32.48717949 -10.9 1.8 1.01282051] [-20.84615385 7.1 -1.2 -0.65384615] [ 3.41025641 -1.1 0.2 0.08974359]] Inverse array is [[1.]]
Example 2:
Python3
# Import required package import numpy as np # Inverses of several matrices can # be computed at once A = np.array([[[1., 2.], [3., 4.]], [[1, 3], [3, 5]]]) # Calculating the inverse of the matrix print(np.linalg.inv(A)) |
Output:
[[[-2. 1. ] [ 1.5 -0.5 ]] [[-1.25 0.75] [ 0.75 -0.25]]]
