Finding the matrix condition number using LU decomposition.

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

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

public class MatrixConditionNumber {

    public static void main(String[] args) {

        double[][] matrixData = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };

        RealMatrix matrix = MatrixUtils.createRealMatrix(matrixData);

        LUDecomposition luDecomposition = new LUDecomposition(matrix);

        RealMatrix luMatrix = luDecomposition.getL().multiply(luDecomposition.getU());

        double conditionNumber = luMatrix.getNorm() * luDecomposition.getSolver().getInverse().getNorm();

        System.out.println("Matrix Condition Number: " + conditionNumber);

    }
}

In this example, we’re using the Apache Commons Math library (`org.apache.commons.math3.linear`) to perform LU decomposition and calculate the condition number. You can include the library in your project by adding the appropriate JAR file or dependency.

The program starts by creating a 3×3 matrix using the input data. Then, it performs LU decomposition on the matrix using `LUDecomposition` from the Apache Commons Math library. The LU matrix is obtained by multiplying the lower triangular matrix (`L`) and the upper triangular matrix (`U`). Finally, the condition number is calculated by multiplying the norm of the LU matrix with the norm of its inverse obtained from the solver.

The result is printed to the console as the matrix condition number.

Note: Make sure you have the Apache Commons Math library added to your project for the code to compile and run successfully.