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-la form a basis for. Let a be any non –Ζ (α; Τ .(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: . Let a be any non – zero vector in V…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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. 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 for Z (а; T). (iii) If U is the linear operator on Z (a; T) induced by T, then the minimal polynomial for U is pa.
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. Let a be any non – zero vector in V and let p. 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-la form a basis for 7 (a : T)