Python Coding challenge - Day 425| What is the output of the following Python Code?

 Code Explanation:

1. Importing Libraries

from scipy.linalg import eig

import numpy as np

numpy is used to define arrays and matrices.

scipy.linalg.eig is used to compute eigenvalues and eigenvectors of a square matrix.

2. Define Matrix A

A = np.array([[0, -1],

              [1,  0]])

This is a special 2x2 matrix known as a rotation matrix. It rotates vectors 90° counter-clockwise.

3. Compute Eigenvalues and Eigenvectors

eigenvalues, _ = eig(A)

eig() returns a tuple: (eigenvalues, eigenvectors)

We're only using the eigenvalues part here.

4. Print Eigenvalues

print(eigenvalues)

The output will be:

[0.+1.j 0.-1.j]

These are complex eigenvalues:

0 + 1j → the complex number i

0 - 1j → the complex number −i

What Do These Eigenvalues Mean?

These eigenvalues lie on the unit circle in the complex plane (|λ| = 1).

They indicate that the transformation (matrix A) rotates vectors by 90 degrees.

Since A represents a rotation matrix, it has no real eigenvalues, because there's no real vector that stays on its own line after being rotated 90°.

Final Output:

[1j,-1j]