. Let a be any non –zero vector in V and let pa be the T- annihilator of a.(i) The degree of pa is equal to the dimension of the cyclic subspace Z (a ; T).(ii) If the degree of pa is k, then the vectors a, Ta, T²a, . . . , Tk-1a form a basis forZ (а; T).(iii) If U is the linear operator on Z (a; T) induced by T, then the minimal polynomialfor U is pa.

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Answered: ) The degree of pa is equal to the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.2: Orthogonal Complements And Orthogonal Projections

Problem 17EQ

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) The degree of pa is equal to the dimension of the cyclic subspace Z (a ; T) .