Solved: Let T be a linear operator on a finite-dimensional vector space, and suppose

Chapter 7, Problem 13

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Let T be a linear operator on a finite-dimensional vector space, and suppose that the characteristic polynomial of T splits. Let Ai, A2 ,..., Afc be the distinct eigenvalues of T, and for each i let pi be the order of the largest Jordan block corresponding to Xi in a Jordan canonical form of T. Prove that the minimal polynomial of T is

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