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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please see attached Advanced Linear Algebra question below. 

 

How to properly prove that λ is an eigenvalue of T if and only if λ is an eigenvalue of [T]β?

 

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We know that
Tv = Xv
is equivalent to
*[a]Y = [a]®[L]
Transcribed Image Text:We know that Tv = Xv is equivalent to *[a]Y = [a]®[L]
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.
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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