NumPy: Compute the condition number of a given matrix

Last update on December 21 2024 07:51:38 (UTC/GMT +8 hours)

Write a NumPy program to compute the condition number of a given matrix.

From Wikipedia: In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an error in the input.

Sample Solution:

Python Code :

# Importing the NumPy library
import numpy as np

# Create a 2x2 NumPy array 'm' containing specific values
m = np.array([[1, 2], [3, 4]])

# Display the original matrix 'm'
print("Original matrix:")
print(m)

# Calculate the condition number of the matrix 'm' using np.linalg.cond() function
result = np.linalg.cond(m)

# Display the condition number of the matrix 'm'
print("Condition number of the said matrix:")
print(result)

Sample Output:

Original matrix:
[[1 2]
 [3 4]]
Condition number of the said matrix:
14.9330343737

Explanation:

In the above code –

m = np.array([[1,2],[3,4]]): This code creates a 2x2 NumPy array m with the specified elements.

result = np.linalg.cond(m): This code computes the condition number of the matrix m. The condition number of a matrix is a scalar value that provides an estimate of how sensitive a linear system is to small changes in its input values. It is calculated as the ratio of the largest singular value to the smallest singular value of the matrix.

Python-Numpy Code Editor: