9. Let T be an operator on an n-dimensional vector space V over a field F. (a) If T has n distinct eigenvalues prove that T is diagonalizable. If T is diagonaziable prove that the characteristic polynomial of T splits over F. (c) Give an example of an operator T such that the characteristic polynomial of T splits but T is not diagonalizable.

9. Let T be an operator on an n-dimensional vector space V over a field F. (a) If T has n distinct eigenvalues prove that T is diagonalizable. If T is diagonaziable prove that the characteristic polynomial of T splits over F. (c) Give an example of an operator T such that the characteristic polynomial of T splits but T is not diagonalizable.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 35E

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