Orthogonal and Singular Matrix with Python | Orthogonal Matrix | Singular Matrix - P11

Orthogonal and Singular Matrix with Python | Orthogonal Matrix | Singular Matrix
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'''12. Orthogonal Matrix'''
'''This example will show that the following matrix is not orthogonal '''

Code Starts Here
==============

import numpy as np

matrix = np.random.randint(0,9,(4,4))
print(matrix)

matrix_transpose = matrix.T
print(matrix_transpose)

print(matrix.dot(matrix_transpose))

This example will show the matrix is orthogonal for unit matrix

umatrix = np.eye(4,4)
print(umatrix)

matrix_transpose=umatrix.T
print(matrix_transpose)
print(umatrix.dot(matrix_transpose))

Show that matrix is orthognal for non unit matrix
from scipy.stats import ortho_group

m = ortho_group.rvs(dim=4)

print(m)

np.set_printoptions(suppress=True)

print(m.dot(m.T))

print(m.T)
print(np.linalg.inv(m))

13. Singular Matrix

This will show that determinant is non-zero and hence not singular
import numpy as np
matrix = np.random.randint(0,9,(4,4))
print(matrix)

print(np.linalg.det(matrix.T.dot(matrix)))

This will show that determinant is zero and hence singular

matrix = np.eye(3,3)
matrix1 = np.ones((3,4))
matrix1[:,:-1] = matrix

np.linalg.det(matrix1.T.dot(matrix1))

matrix = np.zeros(shape=(10,10))
print(matrix)
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