Matrix Multiplication Algorithm

In this section we will see how to multiply two matrices. The matrix multiplication can only be performed, if it satisfies this condition. Suppose two matrices are A and B, and their dimensions are A (m x n) and B (p x q) the resultant matrix can be found if and only if n = p. Then the order of the resultant matrix C will be (m x q).

Algorithm

matrixMultiply(A, B):
Assume dimension of A is (m x n), dimension of B is (p x q)
Begin
   if n is not same as p, then exit
   otherwise define C matrix as (m x q)
   for i in range 0 to m - 1, do
      for j in range 0 to q – 1, do
         for k in range 0 to p, do
            C[i, j] = C[i, j] + (A[i, k] * A[k, j])
         done
      done
   done
End

Example

 Live Demo

#include<iostream>
using namespace std;
int main() {
   int product[10][10], r1=3, c1=3, r2=3, c2=3, i, j, k;
   int a[3][3] = {
      {2, 4, 1},
      {2, 3, 9},
      {3, 1, 8}
   };
   int b[3][3] = {
      {1, 2, 3},
      {3, 6, 1},
      {2, 4, 7}
   };
   if (c1 != r2) {
      cout<<"Column of first matrix should be equal to row of second matrix";
   } else {
      cout<<"The first matrix is:"<<endl;
      for(i=0; i<r1; ++i) {
         for(j=0; j<c1; ++j)
            cout<<a[i][j]<<" ";
         cout<<endl;
      }
      cout<<endl;
      cout<<"The second matrix is:"<<endl;
      for(i=0; i<r2; ++i) {
         for(j=0; j<c2; ++j)
            cout<<b[i][j]<<" ";
         cout<<endl;
      }
      cout<<endl;
      for(i=0; i<r1; ++i)
         for(j=0; j<c2; ++j) {
            product[i][j] = 0;
         }
      for(i=0; i<r1; ++i)
         for(j=0; j<c2; ++j)
            for(k=0; k<c1; ++k) {
               product[i][j]+=a[i][k]*b[k][j];
            }
      cout<<"Product of the two matrices is:"<<endl;
      for(i=0; i<r1; ++i) {
         for(j=0; j<c2; ++j)
            cout<<product[i][j]<<" ";
         cout<<endl;
      }
   }
   return 0;
}

Output

The first matrix is:
2 4 1
2 3 9
3 1 8
The second matrix is:
1 2 3
3 6 1
2 4 7
Product of the two matrices is:
16 32 17
29 58 72
22 44 66