Inverse Matrix
import numpy as np
2x2 example
A = np.array([[7, 4],
[5, 7]])
A_inv = np.linalg.inv(A)
print(A_inv)
3x3 example
B = np.array([[1, 2, 3],
[0, 1, 4],
[5, 6, 0]])
B_inv = np.linalg.inv(B)
print(B_inv)
properties
A^-1 * A = A * A^-1 = I
I1 = np.dot(A, A_inv)
print(I1)
I2 = np.dot(A_inv, A)
print(I2)
(AB)^−1=B^−1A^−1
A = np.array([[2, 1],
[5, 3]])
B = np.array([[1, 2],
[3, 4]])
A_inv = np.linalg.inv(A)
B_inv = np.linalg.inv(B)
AB = np.dot(A, B)
AB_inv = np.linalg.inv(AB)
result = np.dot(B_inv, A_inv)
print(AB_inv)
print(result)
(A^T)^−1=(A^−1)^T
A_T = np.transpose(A)
A_T_inv = np.linalg.inv(A_T)
A_inv_T = np.transpose(A_inv)
print(A_T_inv)
print(A_inv_T)
(kA)^−1=(1/k)(A^−1)
k = 2
kA = k * A
kA_inv = np.linalg.inv(kA)
scaled_result = (1 / k) * A_inv
print(kA_inv)
print(scaled_result)
(A^−1)^−1=A
A_double_inv = np.linalg.inv(A_inv)
print(A_double_inv)
