Multiplication of Matrices

If A and B are two matrices such that the number of columns of A is equal to the number of rows in B, i.e. A = [aik] is a mx n matrix and B =[bkej ] be a nx p matrix then the product AB of these matrices is mx p matrix and is defined as =

if , (AB);j = { aj ij Σ dikbkej = 2;1 b1; +a;2b2; + ... + ainbni n -

k=1

- =

[a il di2 ... Ain]

bi bzi

:

bni

of A with

Sum of the product of elements of ith row the corresponding elements of jth column of B.

Note In

the matrix product AB, the matrix A is called pre multiplier or pre factor and B is called post multiplier or post factor.