Program to find transpose of a matrix

Transpose of a matrix is obtained by changing rows to columns and columns to rows. In other words, transpose of A[][] is obtained by changing A[i][j] to A[j][i].

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For Square Matrix: The below program finds transpose of A[][] and stores the result in B[][], we can change N for different dimension.  

C++

// C++ Program to find
// transpose of a matrix
#include <bits/stdc++.h>
using namespace std;
#define N 4

// This function stores transpose of A[][] in B[][]
void transpose(int A[][N], int B[][N])
{
    int i, j;
    for (i = 0; i < N; i++)
        for (j = 0; j < N; j++)
            B[i][j] = A[j][i];
}

// Driver code
int main()
{
    int A[N][N] = { {1, 1, 1, 1},
                    {2, 2, 2, 2},
                    {3, 3, 3, 3},
                    {4, 4, 4, 4}};

    int B[N][N], i, j;

    transpose(A, B);

    cout <<"Result matrix is \n";
    for (i = 0; i < N; i++)
    {
        for (j = 0; j < N; j++)
           cout <<" "<< B[i][j];
        cout <<"\n";
    }

    return 0;
}

// This code is contributed by shivanisinghss2110

C

// C Program to find
// transpose of a matrix
#include <stdio.h>
#define N 4

// This function stores transpose of A[][] in B[][]
void transpose(int A[][N], int B[][N])
{
    int i, j;
    for (i = 0; i < N; i++)
        for (j = 0; j < N; j++)
            B[i][j] = A[j][i];
}

int main()
{
    int A[N][N] = { {1, 1, 1, 1},
                    {2, 2, 2, 2},
                    {3, 3, 3, 3},
                    {4, 4, 4, 4}};

    int B[N][N], i, j;

    transpose(A, B);

    printf("Result matrix is \n");
    for (i = 0; i < N; i++)
    {
        for (j = 0; j < N; j++)
           printf("%d ", B[i][j]);
        printf("\n");
    }

    return 0;
}

Java

// Java Program to find
// transpose of a matrix

class GFG
{
    static final int N = 4;

    // This function stores transpose
    // of A[][] in B[][]
    static void transpose(int A[][], int B[][])
    {
        int i, j;
        for (i = 0; i < N; i++)
            for (j = 0; j < N; j++)
                B[i][j] = A[j][i];
    }

    // Driver code
    public static void main (String[] args)
    {
        int A[][] = { {1, 1, 1, 1},
                      {2, 2, 2, 2},
                      {3, 3, 3, 3},
                      {4, 4, 4, 4}};

        int B[][] = new int[N][N], i, j;

        transpose(A, B);

        System.out.print("Result matrix is \n");
        for (i = 0; i < N; i++)
        {
            for (j = 0; j < N; j++)
            System.out.print(B[i][j] + " ");
            System.out.print("\n");
        }
    }
}

// This code is contributed by Anant Agarwal.

Python3

# Python3 Program to find
# transpose of a matrix

N = 4

# This function stores
# transpose of A[][] in B[][]

def transpose(A,B):

    for i in range(N):
        for j in range(N):
            B[i][j] = A[j][i]

# driver code
A = [ [1, 1, 1, 1],
    [2, 2, 2, 2],
    [3, 3, 3, 3],
    [4, 4, 4, 4]]


B = [[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]] # To store result

transpose(A, B)

print("Result matrix is")
for i in range(N):
    for j in range(N):
        print(B[i][j], " ", end='')
    print()

# This code is contributed
# by Anant Agarwal.

C#

// C# Program to find
// transpose of a matrix
using System;

class GFG
{
    static int N = 4;

    // This function stores transpose
    // of A[][] in B[][]
    static void transpose(int [,]A, int [,]B)
    {
        int i, j;
        for (i = 0; i < N; i++)
            for (j = 0; j < N; j++)
                B[i,j] = A[j,i];
    }

    // Driver code
    public static void Main ()
    {
        int [,]A = { {1, 1, 1, 1},
                     {2, 2, 2, 2},
                     {3, 3, 3, 3},
                     {4, 4, 4, 4}};

        int [,]B = new int[N,N];

        // Function calling
        transpose(A, B);

        Console.Write("Result matrix is \n");
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            Console.Write(B[i,j] + " ");
            Console.Write("\n");
        }
    }
}

// This code is contributed by nitin mittal.

PHP

<?php

// This function stores transpose
// of A[][] in B[][]
function transpose(&$A, &$B)
{
    $N = 4;
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            $B[$i][$j] = $A[$j][$i];
}

// Driver code
$A = array(array(1, 1, 1, 1),
           array(2, 2, 2, 2),
           array(3, 3, 3, 3),
           array(4, 4, 4, 4));

$N = 4;

transpose($A, $B);

echo "Result matrix is \n";
for ($i = 0; $i < $N; $i++)
{
    for ($j = 0; $j < $N; $j++)
    {
        echo $B[$i][$j];
        echo " ";
    }
    echo "\n";
}

// This code is contributed
// by Shivi_Aggarwal
?>

Javascript

<script>
// javascript Program to find
// transpose of a matrix
        var N = 4;

    // This function stores transpose
    // of A in B
    function transpose(A , B)
    {
        var i, j;
        for (i = 0; i < N; i++)
            for (j = 0; j < N; j++)
                B[i][j] = A[j][i];
    }

    // Driver code

    var A = [
             [ 1, 1, 1, 1 ],
             [ 2, 2, 2, 2 ],
             [ 3, 3, 3, 3 ],
             [ 4, 4, 4, 4 ] ];

    var B =   Array(4).fill(0);
    for(let i = 0; i < N; i++){
       B[i] = new  Array(N);
     }

    transpose(A, B);

    document.write("Result matrix is <br/>");
    for (let i = 0; i < N; i++)
    {
        for (let j = 0; j < N; j++)
            document.write(B[i][j] + " ");
        document.write("<br/>");
    }

// This code is contributed by gauravrajput1

</script>

Output

Result matrix is 
 1 2 3 4
 1 2 3 4
 1 2 3 4
 1 2 3 4

Time complexity: O(N x N).
Auxiliary Space: O(N x N).

The below program finds transpose of A[][] and stores the result in B[][]. 

C++

// C++ program to find
// transpose of a matrix
#include <bits/stdc++.h>
using namespace std;
#define M 3
#define N 4

// This function stores transpose
// of A[][] in B[][]
void transpose(int A[][N], int B[][M])
{
    int i, j;
    for(i = 0; i < N; i++)
        for(j = 0; j < M; j++)
            B[i][j] = A[j][i];
}

// Driver code
int main()
{
    int A[M][N] = { { 1, 1, 1, 1 },
                    { 2, 2, 2, 2 },
                    { 3, 3, 3, 3 } };

    // Note dimensions of B[][]
    int B[N][M], i, j;

    transpose(A, B);

    cout << "Result matrix is \n";
    for(i = 0; i < N; i++)
    {
        for(j = 0; j < M; j++)
            cout << " " << B[i][j];

        cout << "\n";
    }
    return 0;
}

// This code is contributed by shivanisinghss2110

C

#include <stdio.h>
#define M 3
#define N 4

// This function stores transpose of A[][] in B[][]
void transpose(int A[][N], int B[][M])
{
    int i, j;
    for (i = 0; i < N; i++)
        for (j = 0; j < M; j++)
            B[i][j] = A[j][i];
}

int main()
{
    int A[M][N] = { {1, 1, 1, 1},
                    {2, 2, 2, 2},
                    {3, 3, 3, 3}};

    // Note dimensions of B[][]
    int B[N][M], i, j;

    transpose(A, B);

    printf("Result matrix is \n");
    for (i = 0; i < N; i++)
    {
        for (j = 0; j < M; j++)
        printf("%d ", B[i][j]);
        printf("\n");
    }

    return 0;
}

Java

// Java Program to find
// transpose of a matrix

class GFG
{
    static final int M = 3;
    static final int N = 4;

    // This function stores transpose
    // of A[][] in B[][]
    static void transpose(int A[][], int B[][])
    {
        int i, j;
        for (i = 0; i < N; i++)
            for (j = 0; j < M; j++)
                B[i][j] = A[j][i];
    }

    // Driver code
    public static void main (String[] args)
    {
        int A[][] = { {1, 1, 1, 1},
                      {2, 2, 2, 2},
                      {3, 3, 3, 3}};

        int B[][] = new int[N][M], i, j;

        transpose(A, B);

        System.out.print("Result matrix is \n");
        for (i = 0; i < N; i++)
        {
            for (j = 0; j < M; j++)
            System.out.print(B[i][j] + " ");
            System.out.print("\n");
        }
    }
}

// This code is contributed by Anant Agarwal.

Python3

# Python3 Program to find
# transpose of a matrix

M = 3
N = 4

# This function stores
# transpose of A[][] in B[][]

def transpose(A, B):

    for i in range(N):
        for j in range(M):
            B[i][j] = A[j][i]

# driver code
A = [ [1, 1, 1, 1],
    [2, 2, 2, 2],
    [3, 3, 3, 3]]


# To store result
B = [[0 for x in range(M)] for y in range(N)]

transpose(A, B)

print("Result matrix is")
for i in range(N):
    for j in range(M):
        print(B[i][j], " ", end='')
    print()

C#

// C# Program to find
// transpose of a matrix
 using System;
class GFG {

    static  int M = 3;
    static  int N = 4;

    // This function stores transpose
    // of A[][] in B[][]
    static void transpose(int [,]A, int [,]B)
    {
        int i, j;
        for (i = 0; i < N; i++)
            for (j = 0; j < M; j++)
                B[i,j] = A[j,i];
    }

    // Driver code
    public static void Main ()
    {
        int [,]A = { {1, 1, 1, 1},
                      {2, 2, 2, 2},
                      {3, 3, 3, 3}};

        int [,]B= new int[N,M];

        transpose(A, B);

        Console.WriteLine("Result matrix is \n");
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < M; j++)
            Console.Write(B[i,j] + " ");
            Console.Write("\n");
        }
    }
}

// This code is contributed by nitin mittal

PHP

<?php

// This function stores transpose
// of A[][] in B[][]
function transpose(&$A, &$B)
{
    $N = 4;
    $M = 3;
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $M; $j++)
            $B[$i][$j] = $A[$j][$i];
}

// Driver code

$A = array(array(1, 1, 1, 1),
           array(2, 2, 2, 2),
           array(3, 3, 3, 3));

$N = 4;
$M = 3;
transpose($A, $B);

echo "Result matrix is \n";
for ($i = 0; $i < $N; $i++)
{
    for ($j = 0; $j < $M; $j++)
    {
    echo $B[$i][$j];
    echo " ";
    }
    echo "\n";
}

// This code is contributed
// by Shivi_Aggarwal
?>

Javascript

<script>
// javascript Program to find
// transpose of a matrix
var M = 3;
     var N = 4;

    // This function stores transpose
    // of A in B
    function transpose(A , B) {
        var i, j;
        for (i = 0; i < N; i++)
            for (j = 0; j < M; j++)
                B[i][j] = A[j][i];
    }

    // Driver code

        var A = [ [ 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3, 3 ]];

        var B = Array(N);
        for(i=0;i<N;i++)
        B[i] =Array(M).fill(0);

        transpose(A, B);

        document.write("Result matrix is <br/>");
        for (i = 0; i < N; i++) {
            for (j = 0; j < M; j++)
                document.write(B[i][j] + " ");
            document.write("<br/>");
        }
// This code contributed by Rajput-Ji
</script>

Output

Result matrix is 
 1 2 3
 1 2 3
 1 2 3
 1 2 3

Time complexity: O(M x N).
Auxiliary Space: O(M x N),

In-Place for Square Matrix:

C++

#include <bits/stdc++.h>
using namespace std;

#define N 4

// Converts A[][] to its transpose
void transpose(int A[][N])
{
    for (int i = 0; i < N; i++)
        for (int j = i+1; j < N; j++)
            swap(A[i][j], A[j][i]);
}

int main()
{
    int A[N][N] = { {1, 1, 1, 1},
                    {2, 2, 2, 2},
                    {3, 3, 3, 3},
                    {4, 4, 4, 4}};

    transpose(A);

    printf("Modified matrix is \n");
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
           printf("%d ", A[i][j]);
        printf("\n");
    }

    return 0;
}

Java

// Java Program to find
// transpose of a matrix

class GFG
{
    static final int N = 4;

    // Finds transpose of A[][] in-place
    static void transpose(int A[][])
    {
        for (int i = 0; i < N; i++)
            for (int j = i+1; j < N; j++)
            {
                 int temp = A[i][j];
                 A[i][j] = A[j][i];
                 A[j][i] = temp;
            }
    }

    // Driver code
    public static void main (String[] args)
    {
        int A[][] = { {1, 1, 1, 1},
                      {2, 2, 2, 2},
                      {3, 3, 3, 3},
                      {4, 4, 4, 4}};

        transpose(A);

        System.out.print("Modified matrix is \n");
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            System.out.print(A[i][j] + " ");
            System.out.print("\n");
        }
    }
}

Python3

# Python3 Program to find
# transpose of a matrix

N = 4

# Finds transpose of A[][] in-place
def transpose(A):

    for i in range(N):
        for j in range(i+1, N):
            A[i][j], A[j][i] = A[j][i], A[i][j]

# driver code
A = [ [1, 1, 1, 1],
    [2, 2, 2, 2],
    [3, 3, 3, 3],
    [4, 4, 4, 4]]

 transpose(A)

print("Modified matrix is")
for i in range(N):
    for j in range(N):
        print(A[i][j], " ", end='')
    print()

# This code is contributed
# by Anant Agarwal.

C#

// C# Program to find transpose of
// a matrix
using System;

class GFG {

    static int N = 4;

    // Finds transpose of A[][] in-place
    static void transpose(int [,]A)
    {
        for (int i = 0; i < N; i++)
            for (int j = i+1; j < N; j++)
            {
                int temp = A[i,j];
                A[i,j] = A[j,i];
                A[j,i] = temp;
            }
    }

    // Driver code
    public static void Main ()
    {
        int [,]A = { {1, 1, 1, 1},
                    {2, 2, 2, 2},
                    {3, 3, 3, 3},
                    {4, 4, 4, 4}};

        transpose(A);

        Console.WriteLine("Modified matrix is ");
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
                Console.Write(A[i,j] + " ");

            Console.WriteLine();
        }
    }
}

// This code is contributed by anuj_67.

PHP

<?php
// Converts A[][] to its transpose
function transpose(&$A)
{
    $N = 4;
    for ($i = 0; $i < $N; $i++)
        for ($j = $i + 1; $j < $N; $j++)
            {
                $temp = $A[$i][$j];
                $A[$i][$j] = $A[$j][$i];
                $A[$j][$i] = $temp;
            }
}

// Driver Code
$N = 4;
$A = array(array(1, 1, 1, 1),
            array(2, 2, 2, 2),
           array(3, 3, 3, 3),
           array(4, 4, 4, 4));

transpose($A);

echo "Modified matrix is " . "\n";
for ($i = 0; $i < $N; $i++)
{
    for ($j = 0; $j < $N; $j++)
        echo $A[$i][$j] . " ";
    echo "\n";
}

// This code is contributed
// by Akanksha Rai(Abby_akku)
?>

Javascript

<script>

// JavaScript Program to find
// transpose of a matrix
var N = 4;

    // Finds transpose of A in-place
    function transpose(A) {
        for (i = 0; i < N; i++)
            for (j = i + 1; j < N; j++) {
                var temp = A[i][j];
                A[i][j] = A[j][i];
                A[j][i] = temp;
            }
    }

    // Driver code

        var A = [ [ 1, 1, 1, 1 ],
                  [ 2, 2, 2, 2 ],
                  [ 3, 3, 3, 3 ],
                  [ 4, 4, 4, 4 ] ];

        transpose(A);

        document.write("Modified matrix is <br/>");
        for (i = 0; i < N; i++) {
            for (j = 0; j < N; j++)
                document.write(A[i][j] + " ");
            document.write("\<br/>");
        }

// This code is contributed by aashish1995

</script>

Output

Modified matrix is 
1 2 3 4 
1 2 3 4 
1 2 3 4 
1 2 3 4 

Time complexity: O(N x N).
Auxiliary Space: O(1).  since no extra space has been taken.

Note- Transpose has a time complexity of O(n + m), where n is the number of columns and m is the number of non-zero elements in the matrix. The computational time for transpose of a matrix using identity matrix as reference matrix is O(m*n). Suppose, if the given matrix is a square matrix, the running time will be O(n²).