(c) Conclude that T is orthogonally diagonalizable.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 12EQ: In Exercises 7-12, show that is an eigenvector of A and find one eigenvector corresponding to this...
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Suppose T C → C" is self-adjoint and linear.
(a) Prove that T has at least one real eigenvalue.
(b) Suppose v is an eigenvector for T. Prove that W = span(v) is T-invariant.
(c) Conclude that T is orthogonally diagonalizable.
Transcribed Image Text:Suppose T C → C" is self-adjoint and linear. (a) Prove that T has at least one real eigenvalue. (b) Suppose v is an eigenvector for T. Prove that W = span(v) is T-invariant. (c) Conclude that T is orthogonally diagonalizable.
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