Finding the matrix singular values using SVD.

Here’s an example of a Java program that uses the Apache Commons Math library to find the singular values of a matrix using Singular Value Decomposition (SVD):

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

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

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

public class MatrixSingularValues {

    public static void main(String[] args) {

        // Define the matrix

        double[][] matrixData = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

        // Create a RealMatrix object

        RealMatrix matrix = MatrixUtils.createRealMatrix(matrixData);

        // Perform Singular Value Decomposition

        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);

        // Get the singular values

        double[] singularValues = svd.getSingularValues();

        // Print the singular values

        System.out.println("Singular Values:");

        for (double value : singularValues) {

            System.out.println(value);

        }

    }

}

In this example, we create a 3×3 matrix and perform the Singular Value Decomposition using the `SingularValueDecomposition` class from the Apache Commons Math library. The `getSingularValues()` method returns an array of singular values, which we then print to the console.

Make sure you have the Apache Commons Math library added to your project’s classpath before running this code.