# Matrix Multiplication; Term-by-term Multiplication - HP 48gII User Manual

Graphing calculator.

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
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
, is defined as
ij
p
=
c
ij
=
k
1
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:
⋅B
= A
×
×
m
n
m
p
=
a
b
,
for
i
1
, 2 ,
,
K
ik
kj
. Notice that matrix
×
p
n
=
m
;
j
1
, 2 ,
,
n
.
K
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