Finding the matrix determinant using SVD

Here’s a Java program that calculates the determinant of a matrix using the Singular Value Decomposition (SVD) method:

import Jama.Matrix;

public class MatrixDeterminantSVD {

    public static void main(String[] args) {

        // Define your matrix

        double[][] matrixData = {

            {1, 2, 3},

            {4, 5, 6},

            {7, 8, 9}

        };

        // Create a Jama matrix object

        Matrix matrix = new Matrix(matrixData);

        // Calculate the determinant using SVD

        double determinant = calculateDeterminant(matrix);

        // Print the determinant

        System.out.println("Determinant: " + determinant);

    }

    public static double calculateDeterminant(Matrix matrix) {

        // Perform Singular Value Decomposition

        Matrix[] svd = matrix.svd().getUVD();

        // Extract singular values

        double[] singularValues = svd[1].getColumnPackedCopy();

        // Calculate the determinant as the product of singular values

        double determinant = 1.0;

        for (double singularValue : singularValues) {

            determinant *= singularValue;

        }

        return determinant;

    }

}

In this program, we use the `Jama` library, which provides a `Matrix` class and various matrix operations. You can obtain the `Jama` library from the Jama website (https://math.nist.gov/javanumerics/jama/) and add it to your project’s classpath.

The program defines a 3×3 matrix and then calculates the determinant using the `calculateDeterminant` method. This method performs SVD on the matrix and extracts the singular values. It then calculates the determinant as the product of these singular values. The result is printed to the console.

Note that you need to include the `import Jama.Matrix` statement at the beginning of your program to use the `Matrix` class from the `Jama` library.