Graphics Reference
In-Depth Information
4.19 Summary
Matrices play an important role in representing rotations, especially orthogonal ma-
trices, which is why they have been reviewed in this chapter. The inverse matrix is
also an important concept to grasp as this provides the mechanism for reversing a
rotation or change of frame. We will also come across eigenvectors in later chapters,
which is why they were explained in some detail.
4.19.1 Summary of Matrix Operations
Matrix
(
2
×
2
)
ab
cd
.
A
=
Matrix
(
3
×
3
)
⎡
⎤
ab c
def
gh i
⎣
⎦
.
B
=
Transpose
⎡
⎤
ac
bd
,
adg
beh
cf i
A
T
B
T
⎣
⎦
.
=
=
Identity
⎡
⎤
10
01
,
100
010
001
⎣
⎦
.
I
=
I
=
Adding and subtracting
±
=[
m
row,col
±
n
row,col
]
.
M
N
Multiplying by a scalar
±
λ
M
=[±
λm
row,col
]
.
Product transpose
T
N
T
M
T
.
[
MN
]
=
Sum/difference transpose
T
M
T
N
T
.
[
±
]
=
±
M
N
Determinant
det
A
=|
A
|=
ad
−
bc
det
B
=|
B
|=
aei
+
bf g
+
cdh
−
ceg
−
af h
−
bdi.
