Stat 511
Homework 1  corrected
Spring 2011
Due: 11am, Wednesday Jan 19 (because no class Monday Jan 17)
Please review Ken Koehlers notes on vectors and matrices, available at
http://www.public.iastate.edu/
∼
kkoehler/stat511/sect2.4page.pdf
You may skip/skim (for now) the material on eigen and spectral decompositions (pp 78108).
Note that:
•
Dr. Koehler uses
A
T
to indicate matrix transpose. We will use
A
0
.
•
His notes have SPLUS code. My R code, in matrix.r on the class web site, is very similar.
•
frac
13 on p. 115 should be
1
3
.
I have indicated a few problems that I expect you to use a computer for. You should be able to do
the rest by hand, but I encourage you to check your work with a computer.
Let
A
=
1
2
3
0
1
0
,
B
=

1
5
2

1
, and
C
=
0
1

1
1
2
1
.
1. Calculate
C
0
+
A
2. Calculate
BA
3. Calculate
AB
4. Calculate
tr
(
B
)
5. The property shown by result 1.10(iii) in Dr. Koehler’s notes is sometimes called the cyclical
property of the trace. It can be extended to products of 3 (or more) matrices. For 3 matrices,
it is
tr
(
ABC
) =
tr
(
CAB
) =
tr
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 Spring '08
 Staff
 Linear Algebra, Matrices, Invertible matrix, Dr. Koehler

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