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University of Michigan
Fall 2011
EECS551: Practice Problems 2
Instructor: Sandeep Pradhan
1
State TRUE or FALSE by giving reasons. If you give no reason or a wrong reason, you may not
get credit.
•
The eigen values of matrix
b
5 4
2 5
B
are 1 and 10.
•
The eigen value of a projection matrix is either 1 or
−
1.
•
Consider a Hilbert space
X
of dimension
n
. Let
{
p
1
,...,
p
m
}
be a collection of linearly
independent vectors in
X
. Consider an
m
×
m
matrix
A
, where its (
ij
)th entry is given
by
a
p
i
,
p
j
A
. Then the eigen values of
A
are nonnegative.
•
Let
Q
=
b
1
0
.
5
0
.
5
1
B
.
The maximum value of
x
T
Q
x
such that
x
T
x
= 1 is 2.
•
Let
S
denote the space of all complex valued random variables. Consider the following
function
f
:
S × S →
R
,
f
(
X,Y
) =
E
(5
X
*
Y
)
,
where
*
denotes complex conjugation. This is a valid inner product.
•
Consider an
n
×
n
complexvalued matrix
A
that satis±es
A
=
A
H
. The eigenvalues of
A
are nonnegative.
2
Let
X
denote the set of complexvalued CT signals de±ned on the interval [
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This note was uploaded on 01/10/2012 for the course EECS eecs551 taught by Professor J during the Spring '11 term at University of Michigan.
 Spring '11
 J

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