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Transpose matrix

What Is Transpose of a Matrix

A matrix which is formed by turning all the rows of a given matrix into column and vice-versa then the matrix is said to be Transpose matrix. The transpose of matrix A is written as AT

C Program - Transpose of a Matrix

Let us write a C program to Transpose the user entered matrix

c-transpose-matrix.c
```#include <stdio.h>
int main()
{
int i, j, row1, row2, col1, col2, a[10][10], b[10][10];
printf("Enter the order of matrix up to (10 x 10): \n ");
scanf("%d %d ",&row1, &col1);
printf("\nEnter the Elements of matrix A :\n ");
for(i = 0;i < row1;i++)
{
for(j = 0;j < col1;j++)
{
scanf("%d ",&a[i][j]);
}
}
row2 = col1;
col2 = row1;
for(i = 0;i < row1;i++)
{
for(j = 0;j < col1;j++)
{
b[j][i] = a[i][j];
}
}
printf("\nThe Matrix Transpose is \n ");
for(i = 0;i < row2;i++)
{
for(j = 0;j < col2;j++)
{
printf("%4d",b[i][j]);
}
printf("\n");
}
return 0;
}```
```Enter the order of matrix up to (10 x 10) :
3 3
Enter the Elements of matrix A :
1   2   3
4   5   6
7   8   9
The Matrix Transpose is
1   4   7
2   5   8
3   6   9```

Note:

On seeing line 15 and line 16, we can get clear idea, that column is considered as row whereas row is considered as column.

1. (AT)T= A

The above equation shows that the transpose of a transpose matrix is the original matrix.

2. (rA)T = r * AT

The above equation shows that when a scalar element is multiplied to a matrix, the order of transposition is irrelevant.

3. (A + B)T = AT + BT

The above equation shows that the transpose of two added matrices is the same as the addition of the two transpose matrices.

4. (AB)T = BT * AT

The above equation shows that the transpose of a product of matrices equals the product of their transposes in reverse order.

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