3. Let TЄ L(C2) be a linear operator with only a single eigenvalue, λ = C. Show that p(T) = 0 € L(C²) for p(x) = (x − λ)². Hints: Remember that we cannot assume T is diagonalizable, and that we should not use determinants
3. Let TЄ L(C2) be a linear operator with only a single eigenvalue, λ = C. Show that p(T) = 0 € L(C²) for p(x) = (x − λ)². Hints: Remember that we cannot assume T is diagonalizable, and that we should not use determinants
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:3. Let TЄ L(C2) be a linear operator with only a single eigenvalue, λ = C. Show that
p(T) = 0 € L(C²) for p(x) = (x − λ)².
Hints: Remember that we cannot assume T is diagonalizable, and that we should not
use determinants
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