Finding the rank of a matrix

Here’s a Java program that calculates the rank of a matrix using Gaussian elimination:

  import java.util.Arrays;

   public class MatrixRank {

    public static void main(String[] args) {

        int[][] matrix = {

            {1, 2, 3},

            {4, 5, 6},

            {7, 8, 9}

        };

        int rank = calculateRank(matrix);

        System.out.println("Rank of the matrix: " + rank);

    }

    public static int calculateRank(int[][] matrix) {

        int rowCount = matrix.length;

        int colCount = matrix[0].length;

        int rank = Math.min(rowCount, colCount);

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

            // Check if diagonal element is zero

            if (matrix[row][row] != 0) {

                for (int col = 0; col < rowCount; col++) {

                    if (col != row) {

                        // Making all other elements of current column zero

                        int multiplier = matrix[col][row] / matrix[row][row];

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

                            matrix[col][i] -= matrix[row][i] * multiplier;

                        }

                    }

                }

            } else {

                boolean reduced = false;

                // Find a non-zero element in the same column

                for (int i = row + 1; i < rowCount; i++) {

                    if (matrix[i][row] != 0) {

                        // Swap rows to make the non-zero element at the diagonal

                        int[] temp = matrix[row];

                        matrix[row] = matrix[i];

                        matrix[i] = temp;

                        reduced = true;

                        break;

                    }

                }

                if (!reduced) {

                    // All elements below current row are zero, reduce rank

                    rank--;

                    for (int col = 0; col < rowCount; col++) {

                        matrix[col][row] = matrix[col][rank];

                    }
                }
              row--;

            }

        }

        return rank;
    }
}

In this program, the `calculateRank` method takes a 2D matrix as input and returns the rank of the matrix. It uses the Gaussian elimination algorithm to reduce the matrix to row-echelon form. The rank is determined by counting the number of non-zero rows in the row-echelon form.

In the `main` method, a sample matrix is provided, and the `calculateRank` method is called to find the rank of the matrix. The result is then printed to the console. Feel free to modify the sample matrix or input your own matrix to test the program.