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Q. Show Matrix Multiplication Problem?
Let there be 2 matrices M1 and M2 of sizes a x b and b x c correspondingly. If we multiply M1 and M2 product matrix O will be of size a x c.
The values of elements which are stored in the matrix O are in proportion to the subsequent formula:
O_{ij} = Summation x of (M1_{ix} * M2_{xj}) x=1 to b, where 1
Remember for multiplying a matrix M1 with other matrix M2 number of columns in M1 should be equal to number of rows in M2. The renowned matrix multiplication algorithm on sequential computers occupies O(n^{3}) running time. For multiplication of two 2x2 matrices the algorithm needs 8 multiplication and 4 addition operations. One other algorithm known as Strassen algorithm has been worked out that requires 7 multiplication and 14 addition or subtraction operations. Time complexity of Strassen's algorithm is O(n^{2.81}). The fundamental sequential algorithm is explained below:
Algorithm: Matrix Multiplication
Input// Two Matrices M1 and M2
For I=1 to n
For j=1 to n
{
O_{ij} = 0;
For k=1 to n
O_{ij}= O_{ij} + M1_{ik} * M2_{kj}
End For
}
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