MATH 494: Mathematical Foundations of Machine Learning

Assignment #2

(Due Monday, February 19, 2024)

Write a Python program that illustrates, step-by-step, the process of eigendecomposition. Begin with the matrix . Obtain both square matrices that can be constructed from A. For each of the two cases, obtain the matrices P, D, and P^-1 (same symbols as the ones used in class), and confirm that the product of these three matrices is equal to the original matrix. The results of each step of the computations should be clearly displayed on the screen.

You are allowed to use only the following attributes and functionalities from numpy:

· .T transposition

· .matmul() matrix product

· .linalg.inv() inverse

· .linalg.eig() eigenvalues and eigenvectors