Finding the matrix eigenvectors using Givens rotation.

Here’s an example Java code that uses Givens rotation to find the eigenvectors of a given matrix:

import java.util.Arrays;

public class GivensRotationEigenvectors {

    public static double[][] findEigenvectors(double[][] matrix) {

        int n = matrix.length;

        double[][] eigenvectors = new double[n][n];

        // Initialize eigenvectors matrix as identity matrix

        for (int i = 0; i < n; i++) {

            eigenvectors[i][i] = 1.0;

        }

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

            for (int row = col + 1; row < n; row++) {

                double a = matrix[row][col];

                double b = matrix[col][col];

                double r = Math.sqrt(a * a + b * b);

                double c = b / r;

                double s = -a / r;


                // Apply Givens rotation to both matrix and eigenvectors

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

                    double newMatrixRowJ = c * matrix[col][j] + s * matrix[row][j];

                    double newMatrixRowI = -s * matrix[col][j] + c * matrix[row][j];

                    matrix[col][j] = newMatrixRowJ;

                    matrix[row][j] = newMatrixRowI;

                    double newEigenvectorRowJ = c * eigenvectors[col][j] + s * eigenvectors[row][j];

                    double newEigenvectorRowI = -s * eigenvectors[col][j] + c * eigenvectors[row][j];

                    eigenvectors[col][j] = newEigenvectorRowJ;

                    eigenvectors[row][j] = newEigenvectorRowI;

                }

            }

        }

        return eigenvectors;

    }

    public static void main(String[] args) {

        double[][] matrix = {{2, 1}, {1, 3}}; // Example matrix

        double[][] eigenvectors = findEigenvectors(matrix);

        System.out.println("Eigenvectors:");

        for (double[] vector : eigenvectors) {

            System.out.println(Arrays.toString(vector));

        }

    }

}

In this code, the `findEigenvectors` method takes a square matrix as input and returns a matrix containing the eigenvectors as columns. The Givens rotation algorithm is used to perform the calculations. The `main` method demonstrates how to use the `findEigenvectors` method with an example matrix and prints the resulting eigenvectors.