Transpose of a Matrix in C

What is the Transpose of a Matrix in C?

A transpose of a matrix is obtained by interchanging rows of the original matrix with columns and vice-versa. This could be imagined as if there are two matrices P and Q, such that rows of matrix Q are the columns of matrix P and columns of matrix Q are rows of matrix P, then it is said that the matrix Q is the transpose of matrix P.

This operation can be simply represented as follows:

where i and j represent the rows and columns respectively.

Example –

In this example, the order of the matrix remains the same since it is a square matrix. But, if the order of the original matrix is, say 2×3 then the order of the transposed matrix would be 3×2, as shown in the figure below.

Now, before moving on to the program for finding the transpose of a matrix in C, let us first look at an algorithm to understand the approach to be followed.

Algorithm for Finding Transpose of a Matrix in C

1. Declare and initialize a 2-D array p[a][b] of order axb.
2. Read the matrix p[a][b] from the user.
3. Declare another 2-dimensional array t to store the transpose of the matrix. This array will have the reversed dimensions as of the original matrix.
4. The next step is to loop through the original array and convert its rows to the columns of matrix t.
   • Declare 2 variables i and j.
   • Set both i,j=0
   • Repeat until i<b
     • Repeat until j<a
     • t[i][j] = p[j][i]
     • j=j+1**
   • i=i+1
5. The last step is to display the elements of the transposed matrix t.

C Program to find the Transpose of a Matrix

Output –

The matrix used in the program is the same as that mentioned in the example at the beginning of the article.