# HP F2226A - 48GII Graphic Calculator User Manual Page 330

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
= A
⋅B
, where A = [a
, B =
]
×
×
×
×
m
n
m
p
p
n
ij
m
p
, and C = [c
[b
]
]
. Notice that matrix multiplication is only possible if the
×
×
ij
p
n
ij
m
n
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
a
b
,
for
i
1
, 2 ,
K
,
m
;
j
1
, 2 ,
K
,
n
.
ij
ik
kj
k
=
1
This is the same as saying that the element in the i-th row and j-th column of
the product, C, results from multiplying term-by-term the i-th row of A with the j-
th column of B, and adding the products together. 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:
The matrix-vector multiplication introduced in the previous section can be
thought of as the product of a matrix m×n with a matrix n×1 (i.e., a column
vector) resulting in an m×1 matrix (i.e., another vector). To verify this
assertion check the examples presented in the previous section. Thus, the
vectors defined in Chapter 9 are basically column vectors for the purpose of
matrix multiplication.
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