Let T be an linear operator on a complex vector

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let T be an linear operator on a complex vector
space V. Suppose that B = {v1, v2, ..., v8} is an
ordered basis for V and
2 1
0.
0 0 00
0 2 1
0 0 0 0
0 0 2 0 0 0 0 0
0 0 0 2 0000
0 0 0 0 3 10
0 0 0 0 0 300
0 0 0
0 0
1
0 0 0 0
0 0
[T]B =
(i) Find the characteristic polynomial and the
minimal polynomial of T.
(ii) For each sis 8, express T(vj) as a linear
combination of elements in B.
(iii) Find the eigenvalues of I and bases for the
corresponding eigenspaces.
%3D
Transcribed Image Text:Let T be an linear operator on a complex vector space V. Suppose that B = {v1, v2, ..., v8} is an ordered basis for V and 2 1 0. 0 0 00 0 2 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0000 0 0 0 0 3 10 0 0 0 0 0 300 0 0 0 0 0 1 0 0 0 0 0 0 [T]B = (i) Find the characteristic polynomial and the minimal polynomial of T. (ii) For each sis 8, express T(vj) as a linear combination of elements in B. (iii) Find the eigenvalues of I and bases for the corresponding eigenspaces. %3D
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