Graphics Reference
In-Depth Information
4.6 Multiplying a Matrix by a Scalar
Multiplying a matrix by a scalar
λ
is the same as multiplying an equation by the
same scalar. Therefore,
±
=[±
λa
row,col
]
λ
A
.
For example, if
λ
=
2
12
34
,
A
24
68
.
A
=
=
4.7 Product of Two Matrices
As already mentioned, every element in a matrix has a unique address specified
by its row and column:
a
row,col
where a comma separates the values of
row
and
col
. However, these commas can make the notation very fussy and are not always
employed. For example,
a
11
represents the element for
row
=
1 and
col
=
1, and
a
23
represents the element for
row
3. In this topic, we never need
to manipulate matrices with more that 4 rows or columns, therefore, there is no
confusion.
Matrices have their origins in algebra, therefore matrix algebra must agree with
its algebraic counterpart. Bearing this in mind, let's investigate the product of two
matrices:
=
2 and
col
=
a
11
,
b
11
a
12
b
12
A
=
B
=
a
21
a
22
b
21
b
22
then their product is given by
a
11
b
11
+
.
a
12
b
21
a
11
b
12
+
a
12
b
22
AB
=
a
21
b
11
+
a
22
b
21
a
21
b
12
+
a
22
b
22
For example, given
56
78
,
12
34
A
=
B
=
then
5
×
1
+
6
×
35
×
2
+
6
×
4
AB
=
7
×
1
+
8
×
37
×
2
+
8
×
4
5
+
18
10
+
24
=
+
+
7
24
14
32
23
.
34
=
31
46
