Java Program to Implement Matrix Transposition

Matrix transposition is a mathematical operation that involves swapping the rows and columns of a matrix. In simpler terms, the element in the ithi^{th}ith row and jthj^{th}jth column of the original matrix moves to the jthj^{th}jth row and ithi^{th}ith column in the transposed matrix.

In this article, we’ll walk through how to implement matrix transposition in Java with a clear and concise example.

Steps for Matrix Transposition

1. Input the Matrix: First, create and input a matrix of any size (rows × columns).
2. Create a Transpose Matrix: For every element in the matrix, swap the row and column indices.
3. Display the Result: Print the transposed matrix.

Java Code Implementation

import java.util.Scanner;

public class MatrixTransposition {

    // Method to perform matrix transposition
    public static int[][] transposeMatrix(int[][] matrix) {
        // Get the number of rows and columns of the original matrix
        int rows = matrix.length;
        int cols = matrix[0].length;

        // Create a new matrix for the transposed result (rows and cols are swapped)
        int[][] transposedMatrix = new int[cols][rows];

        // Traverse the original matrix and assign elements to the transposed matrix
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                transposedMatrix[j][i] = matrix[i][j];  // Swap the rows and columns
            }
        }

        return transposedMatrix;
    }

    // Method to print the matrix
    public static void printMatrix(int[][] matrix) {
        for (int[] row : matrix) {
            for (int element : row) {
                System.out.print(element + " ");
            }
            System.out.println();
        }
    }

    public static void main(String[] args) {
        // Initialize Scanner for user input
        Scanner scanner = new Scanner(System.in);

        // Get the matrix dimensions from the user
        System.out.print("Enter the number of rows: ");
        int rows = scanner.nextInt();
        System.out.print("Enter the number of columns: ");
        int cols = scanner.nextInt();

        // Create the matrix and get user input for elements
        int[][] matrix = new int[rows][cols];
        System.out.println("Enter the elements of the matrix:");
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                matrix[i][j] = scanner.nextInt();
            }
        }

        // Display the original matrix
        System.out.println("\nOriginal Matrix:");
        printMatrix(matrix);

        // Get the transposed matrix
        int[][] transposedMatrix = transposeMatrix(matrix);

        // Display the transposed matrix
        System.out.println("\nTransposed Matrix:");
        printMatrix(transposedMatrix);
    }
}

Explanation of the Code

1. Matrix Input
   • We use a Scanner to accept matrix dimensions (rows and columns) from the user.
   • We then create a 2D array (matrix) and fill it with user-provided values.
2. Matrix Transposition
   • The transposeMatrix method takes the original matrix as input and creates a new matrix (transposedMatrix) where the rows and columns are swapped.
   • A nested loop is used to assign values from the original matrix to the transposed one by switching their row and column indices.
3. Printing the Matrix
   • The printMatrix method prints the 2D array row by row.
4. Main Method
   • The main method asks for user input, calls the necessary methods to transpose the matrix, and then prints both the original and the transposed matrices.

Example Output

Conclusion

Matrix transposition is a fundamental concept in linear algebra and is often used in various algorithms, including those involving image processing, machine learning, and graph theory. In Java, transposing a matrix is straightforward using a nested loop and a new 2D array. This program can be expanded to handle more complex operations, but the basic idea remains the same: swapping rows and columns.