Multiplication, Division, and Exponentiation
Signals and Systems with MATLAB
Computing and Simulink
Modeling, Fourth Edition
A
−
19
Copyright
©
Orchard Publications
In Section A.2, the arrays
, such a those that contained the coefficients of polynomi-
als, consisted of one row and multiple columns, and thus are called
row vectors
. If an array has
one column and multiple rows, it is called a
column vector
. We recall that the elements of a row
vector are separated by spaces. To distinguish between row and column vectors, the elements of a
column vector must be separated by semicolons. An easier way to construct a column vector, is to
write it first as a row vector, and then transpose it into a column vector. MATLAB uses the single
quotation character (
′
) to transpose a vector. Thus, a column vector can be written either as
b=[
−
1; 3; 6; 11
]
or as
b=[
−
1
3
6
11]'
As shown below, MATLAB produces the same display with either format.
b=[
−
1; 3; 6; 11
]
b =
-1
3
6
11
b=[
−
1
3
6
11]'
% Observe the single quotation character (‘)
b =
-1
3
6
11
We will now define Matrix Multiplication and Element
−
by
−
Element multiplication.
1
.
Matrix Multiplication
(multiplication of row by column vectors)
Let
and
be two vectors. We observe that
is defined as a row vector whereas
is defined as a col-
umn vector, as indicated by the transpose operator (
′
). Here, multiplication of the row vector
by the column vector
,
is performed with the matrix multiplication operator (*). Then,
(A.5)
a
b
c
…
[
]
A
a
1
a
2
a
3
…
a
n
[
]
=
B
b
1
b
2
b
3
…
b
n
[
]
'
=
A
B
A
B
A*B
a
1
b
1
a
2
b
2
a
3
b
3
…
a
n
b
n
+
+
+
+
[
]
gle value
sin
=
=

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