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
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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.
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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