2. Let T E L(R?) be defined by Tv = Av, where A is the matrix [2/V3] is an eigenvector for T, and show that vị together with vz = [1/V5 [-1/V5 2/V5 form an (a) Show that v = orthonormal basis for R?. (b) Show that T is not self-adjoint. (c) Explain why the results of (a) and (b) do not violate the Real Spectral Theorem.
2. Let T E L(R?) be defined by Tv = Av, where A is the matrix [2/V3] is an eigenvector for T, and show that vị together with vz = [1/V5 [-1/V5 2/V5 form an (a) Show that v = orthonormal basis for R?. (b) Show that T is not self-adjoint. (c) Explain why the results of (a) and (b) do not violate the Real Spectral Theorem.
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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![2. Let T € L(R?) be defined by Tv = Av, where A is the matrix
[2/V5
[1/v5]
orthonormal basis for R?.
[-1/V5]
2/V5
(a) Show that v = Na
is an eigenvector for T, and show that vị together with v2 =
form an
(b) Show that T is not self-adjoint.
(c) Explain why the results of (a) and (b) do not violate the Real Spectral Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F059f8a44-0099-41c0-92e3-ad75d014ebad%2F0edede0c-904a-45a1-b4d4-51d9033f55cb%2Fn8e15w_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let T € L(R?) be defined by Tv = Av, where A is the matrix
[2/V5
[1/v5]
orthonormal basis for R?.
[-1/V5]
2/V5
(a) Show that v = Na
is an eigenvector for T, and show that vị together with v2 =
form an
(b) Show that T is not self-adjoint.
(c) Explain why the results of (a) and (b) do not violate the Real Spectral Theorem.
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