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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
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
import
numpy as np
arr
=
np.array[[[
1
,
2
], [
5
,
6
]]]
inverse_array
=
np.linalg.inv[arr]
print
[
"Inverse array is "
]
print
[inverse_array]
print
[]
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
[]
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
[]
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
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]]]