Math 602 (2011)
Homework 2
1. a)
Find a unitary similarity transformation which brings the lower
triangular matrix
±
a
0
b c
²
to upper triangular form.
b)
Find a unitary similarity transformation which brings
B
=
1 0 1 1 0 1
1 2 0 0 0 0
0 0 2 0 1 1
0 0 1 1 0 0
0 0 0 0 1 0
0 0 0 0 1 1
into upper triangular form.
c)
What are the eigenvalues of
B
?
2.
Suppose that
T
is an 3
×
3
upper triangular
matrix. Show that if
TT
*
=
T
*
T
, then
T
must be diagonal.
Note:
the same result holds for a general
n
×
n
upper triangular matrix.
3.
Let
T
be a linear operator on
V
, and let
h
,
i
be an inner product on
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This note was uploaded on 11/09/2011 for the course MATH 601 taught by Professor Un during the Winter '08 term at Ohio State.
 Winter '08
 un
 Math, Linear Algebra, Algebra

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