Game Development Reference
In-Depth Information
We generally use uppercase bold letters to denote matrices.
Sometimes a matrix will contain a single row or column. We give
the special names
row vector
and
column vector
to describe such matri-
ces. Examples of a row and column vector follow:
u
x
v
vvvv
,
,
,
u
u
1
2
3
4
y
u
z
When using row or column vectors, we only need a single subscript,
and sometimes we use letters as the subscripts used to identify an
entry in the row or column.
Equality, Scalar Multiplication, and Addition
Refer to the following four matrices throughout this subsection:
1
2
1
3
1
5
6
2
1
5
A
B
C
D
2
3
5
8
2
3
6
3
0
0
Two matrices are equal if they are of the same dimension and their
corresponding entries are equal. For example,
A=C
because
A
and
C
have the same dimension and their corresponding entries
are equal. We note that
A
B
and
A
D
because either the corre-
sponding entries are not equal or the matrices are of different
dimensions.
We can multiply a matrix by a scalar by multiplying each entry of
the matrix by the scalar. For example, multiplying
D
by the scalar
k
gives:
k
1
k
2
k
1
k
3
k
D
k
6
k
3
k
0
k
0
If
k
= 2, we have:
2
1
2
2
2
1
2
3
2
4
2
6
k
2
D
2
6
2
3
2
0
2
0
12
6
0
0
Two matrices can be added only if they are of the same dimension.
The sum is found by adding the corresponding entries of the two
matrices together. For example:
1
5
6
2
1
6
5
2
7
7
A
B
2
3
5
8
2
5
3
8
3
5
Search WWH ::
Custom Search