Java Program to Find Transpose of Matrix

The transpose of a matrix is obtained by converting its rows into columns and columns into rows. In other words, for a matrix A, the element at A[i][j] moves to A[j][i].

Illustration

Input: [ [ 1 , 2 , 3 ] ,
[ 4 , 5 , 6 ] ,
[ 7 , 8 , 9 ] ]

Output: [ [ 1 , 4 , 7 ] ,
[ 2 , 5 , 8 ] ,
[ 3 , 6 , 9 ] ]

There are two cases which we will face while transposing the Matrix as mentioned below:

Rectangular Matrix: Number of rows ≠ number of columns
Square Matrix: Number of rows = number of columns

1. Transpose of a Rectangular Matrix

For a rectangular matrix, we need to create a new matrix because the number of rows and columns changes after transposition.

Approach

Create a result matrix with columns rows and rows columns.
Traverse the original matrix.
Store A[i][j] at B[j][i].
Print the transpose matrix.

Java

public class GFG {

    static void transpose(int[][] A, int[][] B) {

        for (int i = 0; i < A.length; i++) {
            for (int j = 0; j < A[i].length; j++) {
                B[j][i] = A[i][j];
            }
        }
    }

    public static void main(String[] args) {

        int[][] A = {
            {1, 2, 3, 4},
            {5, 6, 7, 8},
            {9, 10, 11, 12}
        };

        int rows = A.length;
        int cols = A[0].length;

        // Transposed matrix has cols rows and rows columns
        int[][] B = new int[cols][rows];

        transpose(A, B);

        for (int[] row : B) {
            for (int value : row) {
                System.out.print(value + " ");
            }
            System.out.println();
        }
    }
}

Output

Explanation:

Original matrix has 3 rows and 4 columns.
Transposed matrix has 4 rows and 3 columns.
B[j][i] = A[i][j] swaps the row and column positions.

2. Transpose of a Square Matrix Using Extra Space

For a square matrix, we can also create a separate matrix to store the transpose.

Java

public class GFG {

    static void transpose(int[][] A, int[][] B) {

        for (int i = 0; i < A.length; i++) {
            for (int j = 0; j < A.length; j++) {
                B[j][i] = A[i][j];
            }
        }
    }

    public static void main(String[] args) {

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

        int n = A.length;
        int[][] B = new int[n][n];

        transpose(A, B);

        for (int[] row : B) {
            for (int value : row) {
                System.out.print(value + " ");
            }
            System.out.println();
        }
    }
}

Output

1 4 7 
2 5 8 
3 6 9

3. In-Place Transpose of a Square Matrix

A square matrix can be transposed without creating another matrix. We simply swap the elements above the main diagonal with their corresponding elements below it.

Approach

Start from the first row.
Compare each element with the corresponding element below the main diagonal.
Swap A[i][j] and A[j][i].
Start j from i + 1 to avoid swapping the same elements twice.

Java

public class GFG {

    static void transpose(int[][] A) {

        for (int i = 0; i < A.length; i++) {
            for (int j = i + 1; j < A.length; j++) {

                int temp = A[i][j];
                A[i][j] = A[j][i];
                A[j][i] = temp;
            }
        }
    }

    public static void main(String[] args) {

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

        transpose(A);

        for (int[] row : A) {
            for (int value : row) {
                System.out.print(value + " ");
            }
            System.out.println();
        }
    }
}

Try It Yourself

Output

1 4 7 
2 5 8 
3 6 9

Explanation:

A[i][j] is swapped with A[j][i].
The main diagonal elements remain unchanged.
Only the upper triangular part is traversed.
No additional matrix is required.

Java Program to Find Transpose of Matrix

1. Transpose of a Rectangular Matrix

2. Transpose of a Square Matrix Using Extra Space

3. In-Place Transpose of a Square Matrix

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