How to Transpose a Matrix in C

How to Transpose a Matrix in C



Introduction


Matrices play an important part in many mathematical and scientific processes. The transpose is a basic operation on matrices that involves rearranging a matrix's rows and columns. In C programming, comprehending and executing matrix transformation is necessary for effectively managing data conversions and manipulations. We will look at the working approach for constructing the transpose of a matrix in the C programming language. Whether you're new to matrices or an experienced programmer looking to improve your skills, understanding how to transpose a matrix in C.


What is the Transpose Matrix?


The transpose of a matrix is a basic linear algebraic operation with numerous applications in mathematics and computing, including the programming language C. The transpose of a matrix in C is obtained by swapping its rows and columns. This method can be beneficial when interacting with matrices in mathematical procedures including solving linear equations, identifying determinants, and conducting matrix transformations. The transpose of a matrix is represented by the letter "T" in the superscript of the matrix.

Declaration of Matrix: Declare the matrix. First, we must define a two-dimensional array to represent our matrix. We may accomplish this by explaining the number of rows and columns as shown below:

int matrix[m][n];

 

Initialize the matrix: The next step is to complete the matrix with values. We can manage this with a nested for loop, as shown below:

for(int i=0; i<m; i++){  

    for(int j=0; j<n; j++){  

        scanf("%d", &matrix[i][j]); //input values using scanf function  

    }  

}  

Transpose the matrix: After we have initialized our matrix, we can transpose it via another nested for loop, like as follows:

 

for(int i=0; i<m; i++){  

    for(int j=0; j<n; j++){  

        int temp = matrix[i][j];  

        matrix[i][j] = matrix[j][i];  

        matrix[j][i] = temp;  

    }  

}  

We swap the matrix's elements along its diagonal. This can be achieved by saving the numerical value of the component at matrix[i][j] in a temporary variable, exchanging the values of matrix[i][j] and matrix[j][i], and then assigning the values of the temporary variable that was saved to matrix[j][i].

Finally, the transpose matrix can be displayed using another nested for loop, as shown below:

for(int i=0; i<n; i++){  

    for(int j=0; j<m; j++){  

        printf("%d ", matrix[i][j]);  

    }  

    printf("\n");  

}  

Example of Transpose Matrix in C

 

Code

#include <stdio.h>

 

void transposeMatrix(int matrix[][3], int rows, int cols) {

int transpose[cols][rows]; // Create a new matrix to store the transpose

for (int i = 0; i < rows; i++) {

for (int j = 0; j < cols; j++) {

transpose[j][i] = matrix[i][j];} // Place the element in transposed position

}

 

// Print the transposed matrix

printf("Transpose Matrix:\n");

for (int i = 0; i < cols; i++) {

for (int j = 0; j < rows; j++) {

printf("%d\t", transpose[i][j]);}

printf("\n");}

}

 

int main() {

int matrix[3][3] = {

{1, 2, 3},

{4, 5, 6},

{7, 8, 9}};

 

printf("Actual Matrix:\n");

for (int i = 0; i < 3; i++) {

for (int j = 0; j < 3; j++) {

printf("%d\t", matrix[i][j]);}

printf("\n");}

 

transposeMatrix(matrix, 3, 3); // Call the transpose function

 

return 0;

}

Output

 

Explanation

In the above C programming example, we calculate the transpose of a square matrix and output both the actual and transposed matrices.

1. We start by adding the standard input-output library and establishing a constant named Numberr with a value of 3 (#define Numberr 3).

2. Next, we build a function called transposeMatrix that accepts a 2D array representing a square matrix of size Numberr x Numberr as input.

3. Using this function, we define two integer-type control variables, ii and ij.

4. The matrix's upper triangle (above the main diagonal) is then iterated over using two nested for loops.

5. The outer loop controls the row number, while the inner loop controls the column number.

  • Each pair of elements at positions (ii, jj) and (jj, ii) has their values swapped and saved in a temporary variable temp.

  • Since the starting value of ii is set to 0, the outer loop begins with row 0. The control is subsequently transferred to the inner loop, where the control variable is ii+1, or 1 to begin with.

  • The inner loop initially stores the element at [0][1] in the temp variable. It then assigns the value of position number [1][0] to the indice [0][1], as well as the temp variable's value to the indice position [0][1.

  • Following this, the value of jj is incremented by one (i.e., jj++), and the inner loop continues to be executed until the value of jj is less than NUMBERR.

  • Once the condition is false, control returns to the outer loop, and the process is repeated for row 1.

6. The matrix's transpose is obtained after nested loop iterations, or when the outer loop condition becomes false.

7. Then, in the main() function, we define and initialize a 3x3 square matrix.

8. We then print the original matrix to the console using two nested for loops and printf() commands.

9. Next, we use the transposeMatrix function, which modifies the original matrix in place to produce its transpose.

10.                        Following the transposition, we employ nested for loops with printf() commands to display the matrix's transpose.

Conclusion

Learning how to calculate the transpose of a matrix in C or mathematics is a fundamental idea with important applications in computing, physical science, and engineering. The transpose of a matrix is simply the output matrix created by switching the rows and columns of the original matrix. When dealing with matrices, whether square or rectangular, it is critical to remember their qualities and characteristics. Delving deeper into the principles of matrix operations, matrix transposition, and algorithms is essential when it comes to efficiently modifying and evaluating data in real-world programming environments.