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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
.,,2,1;,,2,1,
1
njmiforbac
p
k
kjikij
KK ==⋅=
∑
=
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:
Term-by-term multiplication
Term-by-term multiplication of two matrices of the same dimensions is possible
through the use of function HADAMARD. The result is, of course, another
matrix of the same dimensions. This function is available through Function
catalog (‚N), or through the MATRICES/OPERATIONS sub-menu
(„Ø). Applications of function HADAMARD are presented next: