How to Transpose a Matrix in C

# How to Transpose a Matrix in C

Vikram Singh
Assistant Manager - Content
Updated on Jul 11, 2024 11:10 IST

Ever worked with matrices in math? If so, you might have come across the term ‘transpose’. But how do we achieve this in the C programming language? This article breaks down the concept of matrix transposition in C, making it easy for anyone to grasp. Curious to learn how? Let’s dive in!

Transpose of a Matrix is a process of switching its rows and columns. Transpose of a matrix changes the position of the elements of the matrix, but the matrix properties will remain the same.

In simple terms, the transpose of a matrix is interchanging rows and columns. If A is any matrix, then the transpose of the matrix is given by AT.

Must Check: What is C Programming?

Must Check: Types of Matrix

Representation

If A is any matrix of order m x n, then A’s transpose will be n x m.

A = [aij]m x n, then AT = A' = [aij]n x m.

Let’s take an example to get a better understanding of the Transpose of a Matrix.

In this article, we will discuss different methods to transpose how to transpose a matrix in C programming.

## Transpose of a Matrix using Nested for Loop

```#include<stdio.h> int main() { int matrix[3][3] = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} }; int transpose[3][3]; // Transposing the matrix for(int i=0; i<3; i++) { for(int j=0; j<3; j++) { transpose[j][i] = matrix[i][j]; // Swapping rows with columns } } // Printing the transposed matrix printf("Transposed Matrix:\n"); for(int i=0; i<3; i++) { for(int j=0; j<3; j++) { printf("%d ", transpose[i][j]); } printf("\n"); } return 0;}Copy code```

Output

In the above example, we have done the transposition only for a single matrix (i.e., we have defined the matrix). Now let’s generalize the above example. i.e., now we will take the input from the users using the same nested for loop.

```#include<stdio.h> int main() { int m, n; // Get matrix dimensions from user printf("Enter the number of rows and columns: "); scanf("%d %d", &m, &n); int matrix[m][n], transpose[n][m]; // Input matrix values printf("Enter matrix elements:\n"); for(int i=0; i<m; i++) { for(int j=0; j<n; j++) { scanf("%d", &matrix[i][j]); } } // Transposing using nested loops for(int i=0; i<m; i++) { for(int j=0; j<n; j++) { transpose[j][i] = matrix[i][j]; } } // Display the transposed matrix printf("Transposed Matrix:\n"); for(int i=0; i<n; i++) { for(int j=0; j<m; j++) { printf("%d ", transpose[i][j]); } printf("\n"); } return 0;}Copy code```
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Now, we will discuss one another method to transpose a matrix in C programming.

## Transpose of a Matrix using Pointers

```#include<stdio.h>#include<stdlib.h> int main() { int m, n; // Get matrix dimensions from user printf("Enter the number of rows and columns: "); scanf("%d %d", &m, &n); int **matrix, **transpose; // Dynamic memory allocation matrix = (int **)malloc(m * sizeof(int *)); transpose = (int **)malloc(n * sizeof(int *)); for(int i=0; i<m; i++) { matrix[i] = (int *)malloc(n * sizeof(int)); } for(int i=0; i<n; i++) { transpose[i] = (int *)malloc(m * sizeof(int)); } // Input matrix values printf("Enter matrix elements:\n"); for(int i=0; i<m; i++) { for(int j=0; j<n; j++) { scanf("%d", *(matrix + i) + j); } } // Transposing using pointers for(int i=0; i<m; i++) { for(int j=0; j<n; j++) { *(*(transpose + j) + i) = *(*(matrix + i) + j); } } // Display the transposed matrix printf("Transposed Matrix:\n"); for(int i=0; i<n; i++) { for(int j=0; j<m; j++) { printf("%d ", *(*(transpose + i) + j)); } printf("\n"); } // Free allocated memory for(int i=0; i<m; i++) { free(matrix[i]); } for(int i=0; i<n; i++) { free(transpose[i]); } free(matrix); free(transpose); return 0;}Copy code```
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Now, let’s see what we have done in both the above methods.

Explanation

• User Input: In both methods, we took input from the user.
• Matrix Input: We then prompt the user to input the matrix values.
• Transposition:
• In the first method, we use nested loops to transpose the matrix.
• In the second method, we utilize pointers to achieve the same.
• Display: The transposed matrix is then displayed to the user.

Note:

• Memory Allocation: In the second method, we dynamically allocate memory for the matrix and its transpose using pointers.
• Memory Deallocation: In the second method, we free the dynamically allocated memory to prevent memory leaks.

## Conclusion

Transposition is a process of interchanging rows and columns. It plays an important role in computer graphics (transforming 3D models into 2D models), Data Science (data preprocessing, especially when dealing with a tabular dataset), and cryptography (some algorithms use matrix transposition in the encryption or decryption process).

There are different methods to transpose a matrix in C programming. Here, we have discussed two common methods: Nested For Loops and using pointers.

Hope you will like the article.

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## FAQs

What is matrix transposition in C?

Matrix transposition is the process of converting all the rows of a given matrix into columns and vice versa. In C, this can be done by swapping the matrix elements matrix[i][j] with matrix[j][i] in a nested loop structure.

How do I initialize a matrix in C for transposition?

You can initialize a matrix in C using a two-dimensional array, like int matrix[rows][columns];. Fill this matrix with values before transposing.

What is the basic algorithm to transpose a matrix in C?

1. Iterating over each row and column of the matrix. 2. Swapping the elements at indices [i][j] with [j][i]. Note-This approach works well for square matrices. For non-square matrices, you may need a temporary matrix to hold the transposed values.

How can I transpose a non-square matrix in C?

For a non-square matrix, you need a separate matrix to store the transposed matrix because the dimensions will change. Initialize a new matrix with flipped dimensions (rows as columns and vice versa) and copy elements accordingly.

Are there any library functions in C to help with matrix transposition?

Standard C doesn't provide specific library functions for matrix transposition. You'll need to implement the logic manually or use third-party libraries or frameworks that offer matrix operations.