NumPy: Compute the condition number of a given matrix

Last update on March 25 2025 12:18:09 (UTC/GMT +8 hours)

14. Condition Number (Alternate)

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.

For more Practice: Solve these Related Problems:

• Compute the condition number using np.linalg.cond with both 2-norm and infinity norm and compare the results.
• Create a function that identifies whether a matrix is well-conditioned or ill-conditioned based on its condition number.
• Test the condition number computation on randomly generated matrices and analyze the impact of scaling on the condition number.
• Validate the condition number by comparing it with the ratio of the largest and smallest singular values of the matrix.

Python-Numpy Code Editor: