Given a Euclidean space E, if f: E→E is any self fanguidodge door of pas food of go

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 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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Given a Euclidean space E, if f: EE is any self-adjoint linear map,
then every eigenvalue A of fc is real and is actually an eigenvalue of f (which means that
there is some real eigenvector u EE such that f(u) = Au). Therefore, all the eigenvalues of
f are real.
Transcribed Image Text:Given a Euclidean space E, if f: EE is any self-adjoint linear map, then every eigenvalue A of fc is real and is actually an eigenvalue of f (which means that there is some real eigenvector u EE such that f(u) = Au). Therefore, all the eigenvalues of f are real.
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