Question

Q1: Write a Python program in jupyter that performs diagonalization. It should take a matrix from input and compute PAP. Do not use any built-in function for performing diagonalization. You can use built-in functions for eigen values and eigen vectors. Q2: Write a python program in jupyter for decomposition scalar transformation. For example, if a transformation matrix A is provided as input, the output states which vectors are scaled by what factors under that transformation matrix. Q3: Write a python program in jupyter that computes the null space and column space of a matrix. Do not use any other package except for NumPy.

Answer 1

The SVD is calculated via iterative numerical methods.

Every rectangular matrix has a singular value decomposition, although the resulting matrices may contain complex numbers and the limitations of floating-point arithmetic may cause some matrices to fail to decompose neatly.

Explanation:

import numpy as np

from numpy.linalg import eig

a = np.array([[0, 2],  

             [2, 3]])

w,v=eig(a)

print('E-value:', w)

print('E-vector', v)

from numpy import array

from scipy.linalg import svd

# define a matrix

A = array([[1, 2], [3, 4], [5, 6]])

print(A)

# SVD

U, s, VT = svd(A)

print(U)

print(s)