Transpose a Matrix in C: Program to Find Matrix Transpose

Introduction

In this tutorial, we will learn how to write a C program to transpose a matrix.

The transpose of a matrix is obtained by interchanging its rows and columns. If a matrix has dimensions r × c, its transpose will have dimensions c × r.

Matrix transposition is used in many real-world applications, such as:

• Image Processing: Rotating images (transpose + flip)
• Data Science: Converting data format (rows to columns)
• Computer Graphics: Matrix transformations
• Linear Algebra: Solving systems of equations

Visual Example

For a 2×3 matrix:

[1  2  3]
[4  5  6]

[1  4]
[2  5]
[3  6]

C Program to Transpose a Matrix

#include <stdio.h>

int main() {
    int rows, cols, i, j;
    
    // Ask user for matrix dimensions
    printf("Enter the number of rows: ");
    scanf("%d", &rows);
    printf("Enter the number of columns: ");
    scanf("%d", &cols);
    
    // Declare original and transposed matrices
    int matrix[rows][cols];
    int transpose[cols][rows];
    
    // Read elements into the original matrix
    printf("\nEnter %d elements:\n", rows * cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("matrix[%d][%d] = ", i, j);
            scanf("%d", &matrix[i][j]);
        }
    }
    
    // Transpose the matrix (swap rows and columns)
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            transpose[j][i] = matrix[i][j];
        }
    }
    
    // Display original matrix
    printf("\n=== Original Matrix (%d×%d) ===\n", rows, cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d\t", matrix[i][j]);
        }
        printf("\n");
    }
    
    // Display transposed matrix
    printf("\n=== Transposed Matrix (%d×%d) ===\n", cols, rows);
    for(i = 0; i < cols; i++) {
        for(j = 0; j < rows; j++) {
            printf("%d\t", transpose[i][j]);
        }
        printf("\n");
    }
    
    return 0;
}

Sample Output

Enter the number of rows: 2
Enter the number of columns: 3

Enter 6 elements:
matrix[0][0] = 1
matrix[0][1] = 2
matrix[0][2] = 3
matrix[1][0] = 4
matrix[1][1] = 5
matrix[1][2] = 6

=== Original Matrix (2×3) ===
1	2	3
4	5	6

=== Transposed Matrix (3×2) ===
1	4
2	5
3	6

Example with a Square Matrix:

Enter the number of rows: 3
Enter the number of columns: 3

Enter 9 elements:
matrix[0][0] = 1
matrix[0][1] = 2
matrix[0][2] = 3
matrix[1][0] = 4
matrix[1][1] = 5
matrix[1][2] = 6
matrix[2][0] = 7
matrix[2][1] = 8
matrix[2][2] = 9

=== Original Matrix (3×3) ===
1	2	3
4	5	6
7	8	9

=== Transposed Matrix (3×3) ===
1	4	7
2	5	8
3	6	9

Program Explanation

Let's break down the code step by step:

1. Include Header File: #include <stdio.h> includes the standard input/output library.
2. Declare Variables:
   • int rows, cols; — dimensions of the matrix
   • int i, j; — loop counters
3. Declare Matrices:
   • int matrix[rows][cols]; — original matrix
   • int transpose[cols][rows]; — transposed matrix (dimensions are swapped)
4. Read Matrix: Uses nested loops to read elements into the original matrix.
5. Transpose Operation: The nested loops iterate through the original matrix and assign matrix[i][j] to transpose[j][i], effectively swapping rows and columns.
6. Display Matrices: Prints both the original and transposed matrices.
7. Return: return 0; indicates successful program execution.

Algorithm to Transpose a Matrix

Step-by-step algorithm:

1. Start
2. Read the number of rows (r) and columns (c)
3. Read r × c elements into the matrix
4. Create a transpose matrix of size c × r
5. For i = 0 to r-1:
   • For j = 0 to c-1:
     • transpose[j][i] = matrix[i][j]
6. Print the original matrix
7. Print the transposed matrix
8. End

In-Place Transpose for Square Matrices (No Extra Space)

For square matrices, we can transpose in-place without using an extra matrix:

#include <stdio.h>

int main() {
    int n, i, j, temp;
    
    printf("Enter the size of the square matrix: ");
    scanf("%d", &n);
    
    int matrix[n][n];
    
    printf("\nEnter %d elements:\n", n * n);
    for(i = 0; i < n; i++) {
        for(j = 0; j < n; j++) {
            scanf("%d", &matrix[i][j]);
        }
    }
    
    // In-place transpose for square matrix
    for(i = 0; i < n; i++) {
        for(j = i + 1; j < n; j++) {
            // Swap matrix[i][j] with matrix[j][i]
            temp = matrix[i][j];
            matrix[i][j] = matrix[j][i];
            matrix[j][i] = temp;
        }
    }
    
    printf("\n=== Transposed Matrix (In-Place) ===\n");
    for(i = 0; i < n; i++) {
        for(j = 0; j < n; j++) {
            printf("%d\t", matrix[i][j]);
        }
        printf("\n");
    }
    
    return 0;
}

Sample Output:

Enter the size of the square matrix: 3

Enter 9 elements:
1 2 3
4 5 6
7 8 9

=== Transposed Matrix (In-Place) ===
1	4	7
2	5	8
3	6	9

How In-Place Transpose Works

• Only iterates over the upper triangle of the matrix (i < j)
• Swaps matrix[i][j] with matrix[j][i]
• The diagonal elements (i == j) remain unchanged
• Time Complexity: O(n²)
• Space Complexity: O(1) — no extra matrix needed

Time and Space Complexity

#include <stdio.h>

int main() {
    int rows, cols, i, j;
    
    printf("Enter the number of rows: ");
    scanf("%d", &rows);
    printf("Enter the number of columns: ");
    scanf("%d", &cols);
    
    int matrix[rows][cols];
    
    printf("\nEnter %d elements:\n", rows * cols);
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            scanf("%d", &matrix[i][j]);
        }
    }
    
    // Display transpose by printing columns as rows
    printf("\n=== Transposed Matrix (%d×%d) ===\n", cols, rows);
    for(i = 0; i < cols; i++) {
        for(j = 0; j < rows; j++) {
            printf("%d\t", matrix[j][i]);
        }
        printf("\n");
    }
    
    return 0;
}

Frequently Asked Questions

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