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Matrix-vector multiplication
Matrix-vector multiplication is possible only if the number of columns of the
matrix is equal to the length of the vector. A couple of examples of matrix-
vector multiplication follow:
Vector-matrix multiplication, on the other hand, is not defined. This
multiplication can be performed, however, as a special case of matrix
multiplication as defined next.
Matrix multiplication
Matrix multiplication is defined by C
m
×
n
= A
m×p
⋅B
p×n
. Notice that matrix
multiplication is only possible if the number of columns in the first operand
is equal to the number of rows of the second operand. The general term in
the product, c
ij
, is defined as
Matrix multiplication is not commutative, i.e., in general, A⋅B ≠ B⋅A.
Furthermore, one of the multiplications may not even exist. The following
screen shots show the results of multiplications of the matrices that we
stored earlier:
.,,2,1;,,2,1,
1
njmiforbac
p
k
kjikij
KK ==⋅=
∑
=
SG49A.book Page 5 Friday, September 16, 2005 1:31 PM