Finding the matrix rank using Cholesky decomposition.

Here’s an example of a Java program that finds the rank of a matrix using Cholesky decomposition:

import java.util.Arrays;

public class MatrixRankUsingCholesky {

    public static int getRank(double[][] matrix) {

        int rows = matrix.length;

        int cols = matrix[0].length;

        int rank = Math.min(rows, cols);

        double[][] cholesky = new double[rows][cols];

        for (int i = 0; i < rows; i++) {

            Arrays.fill(cholesky[i], 0.0);

        }

        for (int r = 0; r < rows; r++) {

            for (int c = 0; c < cols; c++) {

                double sum = matrix[r][c];

                for (int j = 0; j < c; j++) {

                    sum -= cholesky[c][j] * cholesky[r][j];

                }

                if (r == c) {

                    cholesky[r][c] = Math.sqrt(sum);

                } else if (c < r) {

                    cholesky[r][c] = sum / cholesky[c][c];

                } else {

                    cholesky[r][c] = 0.0;

                }

            }

        }

        int rankCount = 0;

        for (int i = 0; i < rank; i++) {

            if (cholesky[i][i] > 0.0) {

                rankCount++;

            }

        }

        return rankCount;

    }

    public static void main(String[] args) {

        double[][] matrix = {

            {1, 2, 3},

            {4, 5, 6},

            {7, 8, 9}

        };

        int rank = getRank(matrix);

        System.out.println("Matrix Rank: " + rank);

    }

}

In this program, the `getRank` method takes a matrix as input and returns its rank using the Cholesky decomposition technique. The `main` method provides an example usage of the program by creating a sample matrix and printing its rank. You can modify the matrix values in the `main` method to test with different matrices.