Matrix in Python

 

Rank of Matrix

import numpy as np

x = np.matrix("4,5,16,7;2,-3,2,3;,3,4,5,6;4,7,8,9")

print(x)

[[ 4  5 16  7]

 [ 2 -3  2  3]

 [ 3  4  5  6]

 [ 4  7  8  9]]

#numpy.linalg.matrix_rank() - return a rank of a matrix

# Syntax: numpy.linalg.matrix_rank(matrix)

rank_matrix = np.linalg.matrix_rank(x)

print(rank_matrix)

4

Determinant of Matrix

import numpy as np

x = np.matrix("4,5,16,7;2,-3,2,3;,3,4,5,6;4,7,8,9")

print(x)

[[ 4  5 16  7]

 [ 2 -3  2  3]

 [ 3  4  5  6]

 [ 4  7  8  9]]

det_matrix = np.linalg.det(x)

print(det_matrix)

128.00000000000009

Inverse of a Matrix

inverse formula = A-1 = (1/determinant of A) * adj A

numpy.linalg.inv() - return the multiplicative inverse of a matrix Syntax: numpy.linalg.inv(matrix)

A = np.matrix("3,1,2;3,2,5;6,7,8")

print(A)

[[3 1 2]

 [3 2 5]

 [6 7 8]]

Inv_matrix = np.linalg.inv(A)

print(Inv_matrix)

[[ 0.57575758 -0.18181818 -0.03030303]

 [-0.18181818 -0.36363636  0.27272727]

 [-0.27272727  0.45454545 -0.09090909]]