# HP 50g User Manual Page 331

Graphing calculator.

Matrix multiplication
Matrix multiplication is defined by C
= A
B
, where A = [a
]
, B =
m n
m p
p n
ij
m p
[b
]
, and C = [c
]
. 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.
The product of a vector with a matrix is possible if the vector is a row vector,
i.e., a 1 m matrix, which multiplied with a matrix m n produces a 1xn matrix
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