Finding the matrix condition number using SVD

Here’s a Java program that uses Singular Value Decomposition (SVD) to calculate the condition number of a matrix:

import org.apache.commons.math3.linear.MatrixUtils;

import org.apache.commons.math3.linear.SingularValueDecomposition;

public class MatrixConditionNumber {

    public static void main(String[] args) {

        // Define the matrix

        double[][] matrixData = {

            {1.0, 2.0, 3.0},

            {4.0, 5.0, 6.0},

            {7.0, 8.0, 9.0}

        };

        // Create a RealMatrix object

        org.apache.commons.math3.linear.RealMatrix matrix = MatrixUtils.createRealMatrix(matrixData);

        // Perform singular value decomposition

        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);

        // Get the singular values

        double[] singularValues = svd.getSingularValues();

        // Find the maximum and minimum singular values

        double maxSingularValue = singularValues[0];

        double minSingularValue = singularValues[singularValues.length - 1];

        // Calculate the condition number

        double conditionNumber = maxSingularValue / minSingularValue;

        // Print the condition number

        System.out.println("Condition Number: " + conditionNumber);

    }

}

To run this program, you’ll need to have the Apache Commons Math library added to your project. You can download the library from the Apache Commons Math website and add it to your project’s dependencies.

This program creates a 3×3 matrix and performs singular value decomposition using the `SingularValueDecomposition` class from the Apache Commons Math library. It then retrieves the singular values and calculates the condition number by dividing the maximum singular value by the minimum singular value. Finally, it prints the condition number to the console.