25th
Jan

C Program to Find Transpose of a Matrix

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25th Jan, 2023

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Overview:

Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. In this article I will introduce you with the mathematical concept Matrix and transpose of a matrix. After that, I will explain What is an array? and What is Multidimensional Array? Moreover, I will show Demonstration to Find Transpose of a Matrix. At last, I will show a C Program to Find Transpose of a Matrix with output in front of you.

What is Matrix?

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. The matrix of r rows and c column is known as r X c matrix. Matrices are often denoted using capital roman letters such as A, B and C. For example,

What is Transpose of a Matrix?

The transpose of a matrix can be defined as an operation on which you can switch the rows and column indices of a matrix i.e. it flips a matrix over its diagonal. To calculate the transpose of a matrix, simply interchange the rows and columns of the matrix i.e. write the elements of the rows as columns and write the elements of a column as rows. Here, the number of rows and columns in A is equal to number of columns and rows in B respectively. Thus, the matrix B is known as the Transpose of the matrix A. The transpose of matrix A is represented by A′ or AT. The following statement generalizes transpose of a matrix:

If A = [aij]_m×n, then A′ =[aij]_n×m.

Thus, Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given matrix into columns and vice-versa.”

What is an Array?

An array is a container for the collection of items that stores these items at contiguous memory locations. An array is a variable that can store multiple values.

For example, if you want to store 100 integers in a single variable then you can create an array for it.

What is multi dimensional array?

Multidimensional array is an array of arrays. You can declare a two-dimensional (2d) array.

For example, float x[3][4];

Similarly, you can declare a three-dimensional (3d) array. For example, float y[2][4][3];

Demonstration to Find Transpose of a Matrix

transpose matrix

Logic to Find Transpose of a Matrix

Take input a[][] and store elements in a{3,5,8}{3,9,0}
Take input ‘row’ and no of rows(row) as 2
Take input ‘col’ and no of columns(col) as 3
1st iteration for(i=0;i<row;i++) i.e. for(i=0;0<2;i++) Outer loop
1st iteration for(j=0;j<col;j++) i.e. for(j=0;0<3;j++) Inner loop
transpose[j][i]=mat[i][j]; i.e. transpose[0][0]=mat[0][0] i.e. transpose[0][0]=3
2nd iteration for(j=1;j<col;j++) i.e. for(j=1;1<3;j++) Inner loop
transpose[j][i]=mat[i][j]; i.e. transpose[1][0]=mat[0][1] i.e. transpose[1][0]=5
3rd iteration for(j=2;j<col;j++) i.e. for(j=2;1<3;j++) Inner loop
transpose[j][i]=mat[i][j]; i.e. transpose[2][0]=mat[0][2] i.e. transpose[2][0]=8
2nd iteration for(i=1;i<row;i++) i.e. for(i=1;1<2;i++) Outer loop
1st iteration for(j=0;j<col;j++) i.e. for(j=0;0<3;j++) Inner loop
transpose[j][i]=mat[i][j]; i.e. transpose[0][1]=mat[1][0] i.e. transpose[0][1]=3
2nd iteration for(j=1;j<col;j++) i.e. for(j=1;1<3;j++) Inner loop
transpose[j][i]=mat[i][j]; i.e. transpose[1][1]=mat[1][1] i.e. transpose[1][1]=9
2nd iteration for(j=1;j<col;j++) i.e. for(j=1;1<3;j++) Inner loop
transpose[j][i]=mat[i][j]; i.e. transpose[2][1]=mat[1][2] i.e. transpose[2][1]=0
Now we break out of inner loop and then outer loop.
Hence the transpose of the matrix[3,5,8][3,9,0] is tranpose[3,3][5,9][8,0].

C Program to Find Transpose of a Matrix

#include 
int main() {
    int a[10][10], transpose[10][10], r, c, i, j;
    printf("Enter rows and columns: ");
    scanf("%d %d", &r, &c);

    // Assigning elements to the matrix
    printf("\nEnter matrix elements:\n");
    for (i = 0; i < r; ++i)
        for (j = 0; j < c; ++j) {
            printf("Enter element a%d%d: ", i + 1, j + 1);
            scanf("%d", &a[i][j]);
        }

    // Displaying the matrix a[][]
    printf("\nEntered matrix: \n");
    for (i = 0; i < r; ++i)
        for (j = 0; j < c; ++j) {
            printf("%d  ", a[i][j]);
            if (j == c - 1)
                printf("\n");
        }

    // Finding the transpose of matrix a
    for (i = 0; i < r; ++i)
        for (j = 0; j < c; ++j) {
            transpose[j][i] = a[i][j];
        }

    // Displaying the transpose of matrix a
    printf("\nTranspose of the matrix:\n");
    for (i = 0; i < c; ++i)
        for (j = 0; j < r; ++j) {
            printf("%d  ", transpose[i][j]);
            if (j == r - 1)
                printf("\n");
        }
    return 0;
}

Output of the above Program:

When this Program successfully executed then output is shown as follows:

Enter rows and columns: 2 3

Enter matrix elements:

Enter element a11: 3

Enter element a12: 5

Enter element a13: 8

Enter element a21: 3

Enter element a22: 9

Enter element a23: 0

Entered matrix:

3 5 8