Finding the matrix condition number using Cholesky decomposition.

Here’s an example program in Java that calculates the condition number of a matrix using Cholesky decomposition:

import java.util.Scanner;

public class MatrixConditionNumber {

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);

        System.out.print("Enter the size of the square matrix: ");

        int n = scanner.nextInt();

        double[][] matrix = new double[n][n];

        System.out.println("Enter the elements of the matrix row by row:");

        for (int i = 0; i < n; i++) {

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

                matrix[i][j] = scanner.nextDouble();

            }

        }

        // Calculate the Cholesky decomposition

        double[][] cholesky = choleskyDecomposition(matrix);

        // Calculate the condition number

        double conditionNumber = calculateConditionNumber(cholesky);

        System.out.println("The condition number of the matrix is: " + conditionNumber);

        scanner.close();

    }

    // Perform Cholesky decomposition of a matrix

    private static double[][] choleskyDecomposition(double[][] matrix) {

        int n = matrix.length;

        double[][] cholesky = new double[n][n];

        for (int i = 0; i < n; i++) {

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

                double sum = 0.0;

                if (j == i) {

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

                        sum += Math.pow(cholesky[j][k], 2);

                    }

                    cholesky[j][j] = Math.sqrt(matrix[j][j] - sum);

                } else {

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

                        sum += cholesky[i][k] * cholesky[j][k];

                    }

                    cholesky[i][j] = (matrix[i][j] - sum) / cholesky[j][j];

                }

            }

        }

        return cholesky;

    }

    // Calculate the condition number of a matrix

    private static double calculateConditionNumber(double[][] cholesky) {

        int n = cholesky.length;

        double maxEigenvalue = Double.MIN_VALUE;

        double minEigenvalue = Double.MAX_VALUE;

        for (int i = 0; i < n; i++) {

            double eigenvalue = cholesky[i][i];

            maxEigenvalue = Math.max(maxEigenvalue, eigenvalue);

            minEigenvalue = Math.min(minEigenvalue, eigenvalue);

        }

        double conditionNumber = Math.sqrt(maxEigenvalue / minEigenvalue);

        return conditionNumber;

    }

}

In this program, you’ll be prompted to enter the size of the square matrix and then input the elements of the matrix row by row. The program then calculates the Cholesky decomposition of the matrix and uses it to determine the condition number.

Note that this program assumes the input matrix is symmetric and positive definite, as required by the Cholesky decomposition.