Transpose of matrix C Program

Transpose of a matrix is obtained by changing the row elements to column elements and column elements to row elements.

If the order of the matrix ‘A’ is r * c, then the order of transposed matrix ‘A’ will be c * r. If the matrix is a square matrix then the order of original and the transposed matrices will be same.

Below figure explains the transpose of matrix:

In C programming language Transpose of a given matrix(square or non square) can be found in following 2 ways:

• Without using function.
• Using user defined function.

Both the method will work fine. In the second method we are going to pass parameters to function transpose().

Description:

i and j – Loop control variables.
r and c – Number of rows and columns of matrix.
a – Original or input matrix which is a 2 – Dimensional array. Order of matrix ‘a’ is r * c.
t – Transposed matrix which is a 2 – D array. Order of matrix ‘t’ is c * r.
Input : 2 Dimensional array matrix.
Output : Transpose of 2 Dimensional array matrix.

Now let us write an Algorithm and C program to solve the given problem using both methods.

Algorithm to find the transpose of matrix without using function:

STEP 1: START
STEP 2: READ number of rows and columns of matrix
              READ r, c
STEP 3: READ the elements of original matrix
              LOOP from i = 0 to r
              LOOP from j = 0 to c
              READ a(i)(j) 
STEP 4: PRINT the elements of original matrix
              LOOP from i = 0 to r
              LOOP from j = 0 to c
              PRINT a(i)(j) 
STEP 5: Find the transpose of the matrix
              LOOP from i = 0 to r
              LOOP from j = 0 to c
              t(j)(i) = a(i)(j)
STEP 6: PRINT the transposed matrix
              LOOP from i = 0 to c
              LOOP from j = 0 to r
              PRINT a(i)(j) 
STEP 7: END

Example: C program to find the transpose of matrix without using function:

#include<stdio.h>
#include<conio.h>
int main() {
  int a[10][10], t[10][10], r, c, i, j;
  printf("Enter rows and columns of matrix: ");
  scanf("%d %d", &r, &c);
  printf("Enter matrix elements:\n");
  for (i = 0; i < r; ++i)
  for (j = 0; j < c; ++j) 
    scanf("%d", &a[i][j]);
   printf("Entered matrix: \n");
  for (i = 0; i < r; ++i){
  for (j = 0; j < c; ++j) 
    printf("%d\t", a[i][j]);
  printf("\n");
  }
  for (i = 0; i < r; ++i)
  for (j = 0; j < c; ++j) {
    t[j][i] = a[i][j];
  }
  printf("\nTranspose of the matrix:\n");
  for (i = 0; i < c; ++i){
  for (j = 0; j < r; ++j) 
    printf("%d\t", t[i][j]);
   printf("\n");
  }
  getch();
  return 0;
}

Output:

Enter rows and columns of matrix: 2 4
Enter matrix elements:
1 2 3 4
9 8 7 6
Entered matrix:
1 2 3 4
9 8 7 6
Transpose of the matrix:
1 9
2 8
3 7
4 6

Algorithm to find the transpose of matrix using function:

STEP 1: START
STEP 2: READ number of rows and columns of matrix
              READ r, c
STEP 3: READ the elements of original matrix
              LOOP from i = 0 to r
              LOOP from j = 0 to c
              READ a(i)(j) 
STEP 4: PRINT the elements of original matrix
              LOOP from i = 0 to r
              LOOP from j = 0 to c
              PRINT a(i)(j) 
STEP 5: CALL the transpose() function and pass the arguments  a, r and c
              transpose(a, r, c)
                            LOOP from i = 0 to r
                            LOOP from j = 0 to c
                            Find the transpose of the matrix
                            t(j)(i) = a(i)(j)
STEP 6: PRINT the transposed matrix
              LOOP from i = 0 to c
              LOOP from j = 0 to r
              PRINT a(i)(j) 
STEP 7: END

Example: C program to find the transpose of matrix using transpose() user defined function.

#include<stdio.h>
#include<conio.h>
void transpose(int a[10][10], int r, int c)    
{
    int t[10][10],i,j;
    for(i=0;i<r;i++)    
      for(j=0;j<c;j++)
        t[j][i]=a[i][j];     
    printf("Transpose of the matrix:\n");
    for(i=0;i<c;i++){     
        for(j=0;j<r;j++)
            printf("%d\t",t[i][j]);
        printf("\n");
    }
}
int main()
{
    int r,c,a[10][10],i,j;                 
    printf("Enter the number of rows and columns: ");
    scanf("%d %d",&r,&c);   
    printf("Enter elements of the matrix: \n");
    for(i=0;i<r;i++)    
        for(j=0;j<c;j++)
            scanf("%d",&a[i][j]);
    printf("Original matrix is: \n");
    for(i=0;i<r;i++){
        for(j=0;j<c;j++)
            printf("%d\t",a[i][j]);
        printf("\n");
    }
    transpose(a,r,c);  
    getch();
    return 0;
}

Output:

Enter the number of rows and columns: 3 4
Enter elements of the matrix:
2 9 0 4
5 1 5 7
5 4 2 3
Original matrix is:
2 9 0 4
5 1 5 7
5 4 2 3
Transpose of the matrix:
2 5 5
9 1 4
0 5 2
4 7 3

QUIZ:

1] Transpose of a matrix means

1. Rows and columns are interchanged.
2. Number of rows and columns are equal.
3. Its a square matrix.
4. Its a null matrix.

2] Order of transposed matrix is

1. Always same as original matrix.
2. Always different than original matrix.
3. Order is reversed.
4. All the above.

3] To take matrix input we can use.

1. One for loop.
2. Two nested for loops.
3. Two for loops.
4. None of the above.

4] ‘\t’ is

1. Vertical tab.
2. Horizontal tab.
3. New line character.
4. None of the above.

NOTE: Arrays are collection of elements of same type of data. Two dimensional arrays are used to represent matrices. 2 D arrays have two subscripts. Here we are using static arrays to store the matrix elements.