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kl ∑
(AB ) = AB hl (8.3)
kh
h
This result can be also interpreted by observing that the (k, l) element of the
product is the dot product of the k-row of A and the l-column of B.
In MATLAB, we denote the product of the matrices A and B by A*B.

Example 8.1
Write the different routines for performing the matrix multiplication from the
different definitions of the matrix product.

Solution: Edit and execute the following script M-file:

D=[1 2 3; 4 5 6];
E=[3 6 9 12; 4 8 12 16; 5 10 15 20];

F=D*E

F1=zeros(2,4);
for i=1:2
for j=1:4
for k=1:3
F1(i,j)=F1(i,j)+D(i,k)*E(k,j);
end
end
end
F1

F2=zeros(2,4);
for i=1:2
for j=1:4
F2(i,j)=D(i,:)*E(:,j);
end
end
F2

The result F is the one obtained using the MATLAB built-in matrix multipli-
cation; the result F1 is that obtained from Eq. (8.3) and F2 is the answer
obtained by performing, for each element of the matrix product, the dot
product of the appropriate row from the first matrix with the appropriate col-

© 2001 by CRC Press LLC