Math 20820: Homework 11 - University Of Notre Dame
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1Math 20820: Homework 11
Due Friday, Apr. 15.
For the following matrices which are given with respect to the standard basis
for
, answer the following questions about the operator T corresponding to the
matrix:
(a) Is T self-adjoint?
(b) Is T normal?
(c) What are the eigenvalues for T and for T
(d) What are the eigenevectors for T and for T ?
(e) What are the generalized eigenvectors for T and for T ?
(f) What is the Jordan Canonical form for T and for T ?
(g) Does T have an orthonormal basis of eigenvectors? What about T ?
(h) What is T
versus T
?
1.
1 1
A =
.
0 2
2.
4 3
B =
.
3 4
3.
3
4
C =
.
4
3
4.
3 0
1
D =
0 1
0
.
2 0
0
5.
1 1 1
E =
0 1 1
.
0 0 1
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