Finding the matrix determinant using QR decomposition

Here’s an example Java program that uses QR decomposition to find the determinant of a matrix:

import org.apache.commons.math3.linear.Array2DRowRealMatrix;

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

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

public class MatrixDeterminantQR {

    public static void main(String[] args) {

        // Example matrix

        double[][] matrixData = {

            {1, 2, 3},

            {4, 5, 6},

            {7, 8, 9}

        };

        // Create a RealMatrix object from the matrix data

        RealMatrix matrix = new Array2DRowRealMatrix(matrixData);

        // Perform QR decomposition

        QRDecomposition qrDecomposition = new QRDecomposition(matrix);

        // Get the determinant

        double determinant = qrDecomposition.getDeterminant();

        // Print the determinant

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

    }

}

In this program, we use the Apache Commons Math library (`org.apache.commons.math3`) to perform the QR decomposition and calculate the determinant. Make sure you have the Apache Commons Math library added to your project’s dependencies.

The program starts by creating a `RealMatrix` object from the matrix data. Then, the QR decomposition is performed on the matrix using the `QRDecomposition` class. Finally, the determinant is obtained using the `getDeterminant()` method of the `QRDecomposition` object, and it is printed to the console.

You can replace the `matrixData` array with your own matrix values to calculate the determinant of a different matrix.