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MAS 3105
Quiz 7
November 9, 2010
1) Diagonalize the following matrix:
A
=
2 0
0
0 4
−
2
0 1
1
2) Prove that if
A
is diagonalizable, then
A
T
is also diagonalizable. In particular, if
A
=
PDP

1
, then explicitly give the diagonalization of
A
T
in terms of
P
and
D
.
3) Assume that
A
is a diagonalizable
n
×
n
matrix, and it has exactly one eigenvalue (let’s
call it
λ
). Show that
A
=
λI
n
.
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Unformatted text preview: 4) Verify CauchySchwarz on the vectors u = 1 1 1 1 and v = 1 1 âˆ’ 1 . 5) If u = 1 1 1 1 , Fnd all the vectors v such that u Â· v = b u bb v b (in other words, CauchySchwarz inequality is actually an equality)....
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This note was uploaded on 07/29/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.
 Fall '10
 Dreibelbis

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