Transpose of a Matrix in Java

Transpose of a Matrix in Java | Java Program to transpose 2D array | In this post, we will discuss what is the transpose of a matrix and how to write a Java program to find the transpose of a matrix?

What is the Transpose of a Matrix?

Let A =[a_ij] be an m × n matrix. The transpose of A, denoted by A^t, is the n × m matrix obtained by interchanging the rows and columns of A. In other words, if A^t =[b_ij], then b_ij = a_ji for i = 1,2,…,n and j = 1,2,…,m.

For 3×2 Matrix,

Original Matrix
a11 a12
a21 a22
a31 a32

Transpose Matrix
a11 a21 a31
a12 a22 a32

Example using 2×2 matrix:-

     1   2
A = 
     3   4

Then the transpose of a matrix,

     1   3
At = 
     2   4

Java Method to find the transpose of a Matrix

// method to calculate the transpose of a matrix
public static int[][] transposeMatrix(int[][] a) {

   // calculate row and column size
   int row = a.length;
   int column = a[0].length;

   // declare a matrix to store resultant
   int temp[][] = new int[row][column];

   // calculate transpose of matrix
   // outer loop for row
   for (int i = 0; i < row; i++) {
     // inner loop for column
     for (int j = 0; j < column; j++) {
       // formula
       temp[i][j] = a[j][i];
     }
   }

   // return resultant matrix
   return temp;
}

Time Complexity:- O(N²)

Assuming the matrix is a square matrix then the size of the row and column will be similar. Then the above Java method uses two loops (from 1 to n) to find the transpose of the matrix therefore the time complexity for the method is O(N²).

Java Program to Find Transpose of a Matrix

import java.util.Arrays;

public class Matrix {

  // main method
  public static void main(String[] args) {

    // declare and initialize a matrix
    int a[][] = { { 1, 2 }, { 8, 9 } };

    // find row and column size
    int row = a.length;
    int column = a[0].length;

    // declare new matrix to store result
    int transpose[][] = new int[row][column];

    // Transpose of matrix
    transpose = transposeMatrix(a);

    // display all matrices
    System.out.println("A = " + Arrays.deepToString(a));
    System.out.println("Transpose = " + 
                     Arrays.deepToString(transpose));
  }

  // method to calculate the transpose of a matrix
  public static int[][] transposeMatrix(int[][] a) {

    // calculate row and column size
    int row = a.length;
    int column = a[0].length;

    // declare a matrix to store resultant
    int temp[][] = new int[row][column];

    // calculate transpose of matrix
    // outer loop for row
    for (int i = 0; i < row; i++) {
      // inner loop for column
      for (int j = 0; j < column; j++) {
        // formula
        temp[i][j] = a[j][i];
      }
    }

    // return resultant matrix
    return temp;
  }

}

Output:-

A = [[1, 2], [8, 9]]
Transpose = [[1, 8], [2, 9]]

In this program, to display the matrix we had used deepToString() method of the Arrays class, but you can also use the nested loops. See:- Different ways to print array in Java

Program by taking Input from the User

In the above program both matrices A and B were initialized within the program, now let us see another program for transpose of a matrix by taking input value from the end-user using the Scanner class. If you want then you can also use BufferedReader class.

import java.util.Scanner;

public class Matrix {

  // main method
  public static void main(String[] args) {
    
    // create Scanner class object to read input
    Scanner scan = new Scanner(System.in);
    
    // declare variables
    int row = 0;
    int column = 0;
    int a[][] = null; // first matrix
    int transpose[][] = null; // resultant matrix
    
    // ask row and column size
    System.out.println("Enter row and column size: ");
    row = scan.nextInt();
    column = scan.nextInt();

    // initialize matrices
    a = new int[row][column];
    transpose = new int[row][column];
    
    // read matrix A 
    System.out.println("Enter Matrix A: ");
    for(int i=0; i<row; i++) {
      for(int j=0; j<column; j++) {
        // read matrix elements
        a[i][j] = scan.nextInt();
      }
    }

    // transpose of matrix
    transpose = transposeMatrix(a);

    // display resultant matrix
    System.out.println("Transpose =");
    for(int i=0; i<transpose.length; i++) {
      for(int j=0; j<transpose[0].length; j++) {
        System.out.print(transpose[i][j]+" ");
      }
      System.out.println(); // new line
    }
    
    // close Scanner
    scan.close();
  }

  // method to calculate the transpose of a matrix
  public static int[][] transposeMatrix(int[][] a) {

    // calculate row and column size
    int row = a.length;
    int column = a[0].length;

    // declare a matrix to store resultant
    int temp[][] = new int[row][column];

    // calculate transpose of matrix
    // outer loop for row
    for (int i = 0; i < row; i++) {
      // inner loop for column
      for (int j = 0; j < column; j++) {
        // formula
        temp[i][j] = a[j][i];
      }
    }

    // return resultant matrix
    return temp;
    
  }
}

Output:-

Enter row and column size:
3 3
Enter Matrix A:
1 2 3
4 5 6
7 8 9
Transpose =
1 4 7
2 5 8
3 6 9

Inside the main method, first, we had created the Scanner class object to read input value. Then we had initialized the required variables. After then row and column values have been read from the end-user. Later matrix is initialized with the default value and next to that matrix elements are filled in the matrix by taking input values from the end-user. After that transposeMatrix() method is called which returns the transpose of the passed matrix or 2D array. Finally, matrices are displayed on the screen.

See more matrix programs in Java:- 

1. Program to Print 3×3 Matrix 
2. Sum of matrix elements in Java
3. Sum of Diagonal Elements of Matrix in Java 
4. Row sum and Column sum of Matrix in Java
5. Matrix Addition in Java
6. Subtraction of two matrices in Java 
7. Matrix Multiplication in Java
8. Menu-driven program for Matrix operations

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