Finding the matrix cosine function using Taylor series.

Here’s an example Java code for finding the matrix cosine function using Taylor series:

   import java.util.Arrays;

   public class MatrixCosine {

    public static double[][] matrixCosine(double[][] matrix, int iterations) {

        int n = matrix.length;

        double[][] result = new double[n][n];

        for (int i = 0; i < n; i++) {

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

                double element = matrix[i][j];

                double cosine = computeCosine(element, iterations);

                result[i][j] = cosine;

            }

        }

        return result;

    }
    private static double computeCosine(double x, int iterations) {

        double cosine = 1.0;

        double sign = -1.0;

        double power = 2.0;

        double factorial = 2.0;

        for (int i = 1; i <= iterations; i++) {

            sign *= -1;

            power *= x * x;

            factorial *= (2 * i) * (2 * i - 1);

            cosine += (sign * power) / factorial;

        }

        return cosine;

    }

    public static void main(String[] args) {

        double[][] matrix = {

            {1.0, 2.0, 3.0},

            {4.0, 5.0, 6.0},

            {7.0, 8.0, 9.0}

        };

        int iterations = 10;

        double[][] result = matrixCosine(matrix, iterations);

        System.out.println("Matrix Cosine:");

        for (double[] row : result) {

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

        }

    }

}

In this code, the `matrixCosine` method takes a square matrix and the number of iterations as parameters. It computes the cosine of each element in the matrix using the `computeCosine` helper method. The `computeCosine` method uses the Taylor series expansion to approximate the cosine function. The `main` method demonstrates an example usage, where a sample matrix is provided, and the matrix cosine is computed using 10 iterations.

Note that this code assumes that the input matrix is square, meaning the number of rows is equal to the number of columns.