Let T be a linear operator on a finite-dimensional vector space V, and let 3 be an ordered basis for V. Prove that A is an eigenvalue of Tif and only if A is an eigenvalue of (T]a.
Let T be a linear operator on a finite-dimensional vector space V, and let 3 be an ordered basis for V. Prove that A is an eigenvalue of Tif and only if A is an eigenvalue of (T]a.
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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How to properly prove that λ is an eigenvalue of T if and only if λ is an eigenvalue of [T]β?
Please do not reject question if you do not know how to solve this problem. Allow another expert a chance to answer this question.
![We know that
Tv = Xv
is equivalent to
*[a]Y = [a]®[L]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15feef40-32fb-4401-88ed-794608a5d767%2F5b74da03-8099-4287-bddd-27025f5030ef%2Fey55tgl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We know that
Tv = Xv
is equivalent to
*[a]Y = [a]®[L]

Transcribed Image Text:Let T be a linear operator on a finite-dimensional vector space V, and
let 3 be an ordered basis for V. Prove that A is an eigenvalue of T if
and only if A is an eigenvalue of (T3.
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