Finding the singular value decomposition of a matrix.

Here’s an example of a Java program that finds the singular value decomposition (SVD) of a matrix using the Apache Commons Math library:

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

   public class SingularValueDecompositionExample {

    public static void main(String[] args) {

        // Define the input matrix

        RealMatrix matrix = MatrixUtils.createRealMatrix(new double[][] {

            { 1, 2, 3 },

            { 4, 5, 6 },

            { 7, 8, 9 }

        });

        // Perform singular value decomposition

        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);

        // Get the decomposed matrices

        RealMatrix U = svd.getU();

        RealMatrix S = svd.getS();

        RealMatrix V = svd.getV();

        // Print the decomposed matrices

        System.out.println("U matrix:");

        printMatrix(U);

        System.out.println("S matrix:");

        printMatrix(S);

        System.out.println("V matrix:");

        printMatrix(V);

    }

    private static void printMatrix(RealMatrix matrix) {

        double[][] data = matrix.getData();

        for (double[] row : data) {

            for (double value : row) {

                System.out.print(value + "\t");

            }

            System.out.println();

        }

        System.out.println();

    }

}

Make sure you have the Apache Commons Math library added to your project’s dependencies to use the `SingularValueDecomposition` class. You can find the library at https://commons.apache.org/proper/commons-math/.

In this example, we define a 3×3 input matrix and then perform the singular value decomposition using the `SingularValueDecomposition` class. The resulting U, S, and V matrices are then printed to the console using the `printMatrix` helper method.

Remember to replace the input matrix with your desired matrix dimensions and values when using the program.