Transpose of a Matrix in C

The transpose of a matrix is found by interchanging its rows into columns or columns into rows. The transpose of the matrix is denoted by using the letter “T” in the superscript of the given matrix.

For example, if “A” is the given matrix, then the transpose of the matrix is represented by A’ or A^T.

Example 1:
If the given matrix \( A =
\begin{bmatrix}
1 & 2 & 3\\
4 & 5 & 6\\
7 & 8 & 9
\end{bmatrix}\), then the transpose matrix (A^T) is \( \begin{bmatrix}
1 & 4 & 7\\
2 & 5 & 8\\
3 & 6 & 9
\end{bmatrix}\)

Since it is a square matrix, the order of the matrix does not change when it is transposed.

Example 2:
If the order of the original matrix is 2×3, the order of the transposed matrix will be 3×2, as shown below.

If the given matrix \( A =
\begin{bmatrix}
1 & 2 & 3\\
4 & 5 & 6
\end{bmatrix}\), then the transpose matrix (A^T) is \( \begin{bmatrix}
1 & 4 \\
2 & 5\\
3 & 6
\end{bmatrix}\)

Write a C Program to find the transpose of a given matrix.

The transpose of a given matrix is calculated by interchanging the rows and columns of a matrix.

There are two ways to find the transpose of a matrix in C.

• Transpose of a Matrix in C using Loops
• Transpose of a Matrix in C using Loops and Function

In this approach, we iterate over the matrix using two loops and store matrix[i][j] in its transpose[j][i]. Basically we are interchanging rows with columns. The Element at index i,j will now be stored at j,i.

Algorithm:

1. Start the program.
2. Input the order of matrix.
3. Input the elements of the matrix.
4. Store transpose of matrix in a transpose matrix by iterating over complete matrix.
5. End the Program.

Here is source code of the C program to find the transpose of a given matrix using loops (For Loop). The C program is successfully compiled and run on a Linux system. The program output is also shown below.

/*
 * C Program to Find Transpose of a Matrix using Loops
 */
 
#include <stdio.h>
 
void main()
{
    static int array[10][10],transpose[10][10];
    int i, j, m, n;
 
    printf("Enter the order of the matrix \n");
    scanf("%d %d", &m, &n);
    printf("Enter the coefficients of the matrix\n");
    for (i = 0; i < m; ++i)
    {
        for (j = 0; j < n; ++j)
        {
            scanf("%d", &array[i][j]);
        }
    }
    printf("The given matrix is \n");
    for (i = 0; i < m; ++i)
    {
        for (j = 0; j < n; ++j)
        {
            printf(" %d", array[i][j]);
        }
        printf("\n");
    }
    for (i = 0;i < m;i++)
    {
        for (j = 0; j < n; j++)
        {   
            transpose[j][i] = array[i][j];
        }
    }
 
    // printing the transpose of a matrix
    printf("Transpose of matrix is \n");
    for (i = 0; i< n; i++)
    {
        for (j = 0; j < m; j++)
        {
           printf("%d ", transpose[i][j]);
        }
        printf("\n");
    }
}

1. First input the order of the matrix, then take input of elements of the matrix.
2. In this C program, we are reading the order of the matrix row and column using ‘m’ and ‘n’ variables respectively.
3. Using for loop the coefficient elements of the matrix is assigned to the variable array[i][j].
4. Then find out the transpose of the matrix by storing the value of array[i][j] in transpose[j][i] i.e storing values of rows in columns.
5. Then, print the transpose of the matrix.

Time Complexity: O(m*n)
In the program, we are iterating over the complete matrix, so time complexity is O(m*n), where m, n are the rows and columns of the matrix.

Space Complexity: O(m*n)
Space is required to store the transpose of matrix, which is O(m*n), where m, n are the rows and columns of the matrix.

In this case, we enter the order of the matrix as “3 * 3” and the matrix elements as input to find the transpose of a matrix.

Enter the order of the matrix 
3 3
Enter the coefficients of the matrix
1 2 3
4 5 6
7 8 9
The given matrix is 
1 2 3
4 5 6
7 8 9
Transpose of matrix is 
1 4 7
2 5 8
3 6 9

In this approach, we use a function to transpose a matrix. In the function, we traverse the whole matrix and store the value at index i,j in the index j,i of the transpose matrix. Afterwards we print the transpose matrix.

Algorithm to Find Transpose of a Matrix using Loop and Function:
1. Start the program.
2. Input the order of matrix.
3. Input the elements of the matrix.
4. Declare a function to find transpose of the matrix.
5. Call the function.
6. End the Program.

Here is source code of the C program to find the transpose of a given matrix using loops and function. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

/*
 * C Program to Find Transpose of a Matrix using Loops and Function
 */
 
#include <stdio.h>
 
void transpose_matrix(int m,int n, int array[10][10])
{
    //transposing array matrix
    int transpose[10][10];
    for (int i = 0;i < m;i++)
    {
        for (int j = 0; j < n; j++)
        {   
            transpose[j][i] = array[i][j];
        }
    }  
    printf("Transpose of matrix is \n");
    for (int i = 0; i< n; i++)
    {
        for (int j = 0; j < m; j++)
        {
            printf("%d ", transpose[i][j]);
        }
        printf("\n");
    }
}
 
void main()
{
    static int array[10][10];
    int i, j, m, n;
 
    printf("Enter the order of the matrix \n");
    scanf("%d %d", &m, &n);
    printf("Enter the coefficients of the matrix\n");
    for (i = 0; i < m; ++i)
    {
        for (j = 0; j < n; ++j)
        {
            scanf("%d", &array[i][j]);
        }
    }
    printf("The given matrix is \n");
    for (i = 0; i < m; ++i)
    {
        for (j = 0; j < n; ++j)
        {
            printf("%d ", array[i][j]);
        }
        printf("\n");
    }
    transpose_matrix(m,n,array);
}

1. First input the order of the matrix, then take input of elements of the matrix.
2. Then declare a function to find out the transpose of the matrix by storing the value of array[i][j] in transpose[j][i] i.e storing values of rows in columns.
3. Then, execute or call the function.
4. Print the transpose of the matrix.

Time Complexity: O(m*n)
In the program, we are iterating over the complete matrix, so time complexity is O(m*n), where m, n are the rows and columns of the matrix.

Space Complexity: O(m*n)
Space is required to store the transpose of matrix, which is O(m*n), where m, n are the rows and columns of the matrix.

In this case, we enter the order of the matrix as “2 * 3” and the matrix elements as input to find the transpose of a matrix.

Enter the order of the matrix 
2 3
Enter the coefficients of the matrix
1 2 3
4 5 6
The given matrix is 
1 2 3 
4 5 6 
Transpose of matrix is 
1 4 
2 5 
3 6

To practice programs on every topic in C, please visit “Programming Examples in C”, “Data Structures in C” and “Algorithms in C”.