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Let TV → V be an operator with V a f.d.i.p.s. Show that A is an eigenvalue of T if and only if X is an eigenvalue of T*. Why does this mplies that real symmetric matrices has a real eigenvalue?

Let TV → V be an operator with V a f.d.i.p.s. Show that A is an eigenvalue of T if and only if X is an eigenvalue of T*. Why does this mplies that real symmetric matrices has a real eigenvalue?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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Let T : V → V be an operator with V a f.d.i.p.s. Show that λ is an eigenvalue of T if and only if X is an eigenvalue of T*. Why does this implies that real symmetric matrices has a real eigenvalue?
Transcribed Image Text:Let T : V → V be an operator with V a f.d.i.p.s. Show that λ is an eigenvalue of T if and only if X is an eigenvalue of T*. Why does this implies that real symmetric matrices has a real eigenvalue?
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