Question

Write a function spectral_radius that uses the numpy.linalg.eig function to compute the eigenvalues of an input 2-D array A and returns the eigenvalue with the maximum absolute value.

Answer 1

The spectral_radius function calculates the eigenvalues of a matrix A using numpy.linalg.eig and returns the maximum absolute value among these eigenvalues, representing the matrix's spectral radius.

Step-by-step explanation:

The function spectral_radius needs to be written in such a way that it calculates the eigenvalues of a square matrix using the numpy.linalg.eig function and then determines the eigenvalue with the maximum absolute value, which is known as the spectral radius of the matrix.

Here is a sample Python function to achieve this:

import numpy as np

def spectral_radius(A):
eigenvalues, _ = np.linalg.eig(A)
return np.max(np.abs(eigenvalues))

This function accepts a 2-D numpy array A as input, computes its eigenvalues using numpy.linalg.eig, and then returns the maximum absolute value among those eigenvalues, effectively the spectral radius of the matrix.