# Matrix Multiplication and Normalization in C program

## Matrix Multiplication

Now procedure of Matrix Multiplication is discussed. The Matrix Multiplication can only be performed, if it satisfies certain condition. Suppose two matrices are P and Q, and their dimensions are P (a x b) and Q (z x y) the resultant matrix can be found if and only if b = x. Then the order of the resultant matrix R will be (m x q).

## Algorithm

matrixMultiply(P, Q):
Assume dimension of P is (a x b), dimension of Q is (z x y)
Begin
if b is not same as z, then exit
otherwise define R matrix as (a x y)
for i in range 0 to a - 1, do
for j in range 0 to y – 1, do
for k in range 0 to z, do
R[i, j] = R[i, j] + (P[i, k] * Q[k, j])
done
done
done
End

## Matrix Normalization

Suppose we have a 2x3 matrix:
4 5 6
1 2 3 The normalized matrix would be:
4/sqrt(pow(5,2) + pow(6,2)) 5/sqrt(pow(5,2) + pow(6,2)) 6/sqrt(pow(5,2) + pow(6,2))
1/sqrt(pow(2,2) + pow(3,2)) 2/sqrt(pow(2,2) + pow(3,2)) 3/sqrt(pow(2,2) + pow(3,2))

## Example

#include <stdio.h>
#include <math.h>
int main() {
int row, col, row1, col1;
long long int a, square[50] = {0};
double norm[50][50], k;
printf("Enter size of a matrix");
scanf("%d %d", &row, &col);
printf("Enter matrix of size %dX%d", row, col);
for ( row1 = 0; row1 < row; row1++) {
for (col1 = 0; col1 < col; col1++) {
scanf("%d", &assignMatrix[row1][col1]);
}
}
printf("rows: %d cols: %d elements:",row,col);
for( row1 = 0; row1 < row; row1++) {
for( col1 = 0; col1 < col; col1++) {
printf("%d ", assignMatrix[row1][col1]);
}
printf("");
}
for (row1 = 0; row1 < row; row1++) {
for (col1 = 1; col1 < col; col1++) {
a = assignMatrix[r][c];
square[row1] += a * a;
}
printf("Sum of squares of row %d: %lld",row1,square[row1]);
}
for ( row1 = 0; row1 < row; row1++ ) {
k = 1.0 / sqrt(square[row1]);
for( col1 = 0; col1 < col; col1++ ) {
norm[row1][col1] = k * assignMatrix[row1][col1] ;
}
}
printf("Normalized Matrix:");
for( row1 = 0; row1 < row; row1++) {
for( col1 = 0; col1 < col; col1++) {
printf("%.3lf ", norm[row1][col1]);
}
printf("");
}
return 0;
}

## Output

Enter size of a matrix
2
3
Enter matrix of size 2X3
4 5 6
1 2 3
rows: 2 cols: 3 elements:
4 5 6
1 2 3
Sum of squares of row 0: 61
Sum of squares of row 1: 13
Normalized Matrix:
0.512 0.640 0.768
0.277 0.555 0.832
Process returned 0 (0x0) execution time : 12.446 s
Press any key to continue.