MatrixMultiplication Algorithm

ALGORITHM MatrixMultiplication(A[0..n - 1, 0..n - 1], 

B[0..n - 1, 0..n - 1])

//Multiplies two square matrices of order n by the definition-based 

algorithm

//Input: Two n × n matrices A and B

//Output: Matrix C = AB

for i ← 0 to n - 1 do

forj ← 0 to n - 1 do

C[i, j] ← 0.0

for k ← 0 to n - 1 do

C[i, j] ← C[i, j] + A[i, k] ∗ B[k, j]

return C

C program:

#include <stdio.h>

int main()

{

  int m, n, p, q, c, d, k, sum = 0;

  int first[10][10], second[10][10], multiply[10][10];

  printf("Enter number of rows and columns of first matrix\n");  

scanf("%d%d", &m, &n);

  printf("Enter elements of first matrix\n");

  for (c = 0; c < m; c++)

    for (d = 0; d < n; d++)

      scanf("%d", &first[c][d]);

  printf("Enter number of rows and columns of second matrix\n");

  scanf("%d%d", &p, &q);

  if (n != p)

    printf("The matrices can't be multiplied with each other.\n");

  else

  {

    printf("Enter elements of second matrix\n");

    for (c = 0; c < p; c++)

      for (d = 0; d < q; d++)

        scanf("%d", &second[c][d]);

    for (c = 0; c < m; c++) {

      for (d = 0; d < q; d++) {

            multiply[c][d]=0;

        for (k = 0; k < p; k++) {

          multiply[c][d] = multiply[c][d]+ first[c][k]*second[k][d];

        }

    }

    }

    printf("Product of the matrices:\n");

    for (c = 0; c < m; c++) {

      for (d = 0; d < q; d++)

        printf("%d\t", multiply[c][d]);

      printf("\n");

    }

  }

  return 0;

}

Output:

Enter number of rows and columns of first matrix

2

2

Enter elements of first matrix

1

2

3

4

Enter number of rows and columns of second matrix

2

2

Enter elements of second matrix

1

2

3

4

Product of the matrices:

7       10

15      22