Game Development Reference
In-Depth Information
most linear algebra textbooks. However, we certainly know there is a larger
world out there for you. Although traditional linear algebra and systems of
equations do not play a prominent role for basic video game programming,
they are essential for many advanced areas. Consider some of the tech-
nologies that are generating buzz today: fluid, cloth, and hair simulations
(and rendering); more robust procedural animation of characters; real-time
global illumination; machine vision; gesture recognition; and many more.
What these seemingly diverse technologies all have in common is that they
involve di
cult linear algebra problems.
One excellent resource for learning the bigger picture of linear algebra
and scientific computing is Professor Gilbert Strang's series of lectures,
which can be downloaded free from MIT OpenCourseWare at ocw.mit.edu.
He offers a basic undergraduate linear algebra course as well as graduate
courses on computational science and engineering. The companion text-
books he writes for his classes [67, 68] are enjoyable topics aimed at engi-
neers (rather than math sticklers) and are recommended, but be warned
that his writing style is a sort of shorthand that you might have trouble
understanding without the lectures.
4.4
Exercises
(Answers on page 759.)
Use the following matrices for questions 1-3:
2
4
13
3
5
2
4
3
5
4
−8
k
x
0
0
12
0
6
15
8
A =
B =
0
k
y
0
C =
−3 −1
5
−7
3
0
0
k
z
10
−2
5
2
4
3
5
2
4
x
3
5
a
g
b
h
0
y
z
w
D =
c
i
E =
1
3
F =
d
j
f
k
2
4
3
5
α
β
γ
G =
10
20
30
1
H =
1. For each matrix, give the dimensions of the matrix and identify whether it
is square and/or diagonal.
2. Transpose each matrix.
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