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Unformatted text preview: 12. Page 280, Problem 4 Extra Problem The minimal polynomial plays an important role in more advanced subjects of linear algebra. Definition: Let T be a linear operator on a finite-dimensional vector space. Polynomial p ( t ) is a minimal polynomial of T if (i) p ( t ) is monic and (ii) p ( T ) T and (iii) p ( t ) has smallest degree among all polynomials satisfying (i) and (ii). Prove: (a) If g ( t ) is a polynomial for which g ( T ) T , then p ( t ) divides g ( t ) . (b) The minimal polynomial of T is unique....
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- Spring '11