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Exercises
December 8, 2010
1. If the characteristic polynomial of a matrix
A
is (
t
2

4)
2
(
t
+ 1)
5
, then compute the size of the matrix,
its eigenvalues, trace and determinant.
2. Show that (
ST
)
*
=
T
*
S
*
and that (
αT
)
*
=
αT
*
.
3. If
A,B
∈
C
n
, then prove that
(a) trace(
AB
) = trace(
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Unformatted text preview: BA ). (b) trace( αA + B ) = α trace( A ) + trace( B ) 4. Suppose that S ∈ C n × n is an invertible matrix. Show that SAS1 and A have the same characteristic polynomial, eigenvalues, trace, and determinant. 1...
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This document was uploaded on 10/29/2011 for the course MATH 204 at Vanderbilt.
 Fall '08
 STAPLES
 Linear Algebra, Algebra, Determinant

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