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

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