Game Development Reference
In-Depth Information
We choose the constants a , b , and c so that the eigenvectors have unit length. A
quick test verifies that the eigenvectors are orthogonal as expected since the ma-
trix M is symmetric. Define the matrix A as
VV V
1
2
3
A
=
VV V
1
2
3
0
0.851
0.526
.
(3.107)
0
0.526
0.851
10
0
A is an orthogonal matrix that diagonalizes M :
10
0
35
+
AMA AMA
1
=
T
=
0
0
.
(3.108)
2
35
0
0
2
Chapter 3 Summary
Matrix Products
If F is an nm
×
matrix and G is an mp
×
matrix, then the product FG is an np
×
()
matrix whose
, ij entry is given by
m
(
)
FG
=
F G
.
ij
ik
kj
k
=
1
Determinants
The determinant of an nn
×
matrix M is given by the formulas
n
()
det
M
=
MC
M
ik
ik
i
=
1
and
Search Nedrilad ::




Custom Search