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Asked Mar 3, 2020
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Let T be a linear operator on a finite-dimensional vector space V such that the characteristic polynomial of T splits, and let
A1, A2, . .. , Ak be the distinct eigenvalues of T. For each i, let Ji be the Jordan canonical form of the restriction of T to KAi.
Prove that
J = J1 O J2 O -.OJk
is the Jordan canonical form of J.
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Let T be a linear operator on a finite-dimensional vector space V such that the characteristic polynomial of T splits, and let A1, A2, . .. , Ak be the distinct eigenvalues of T. For each i, let Ji be the Jordan canonical form of the restriction of T to KAi. Prove that J = J1 O J2 O -.OJk is the Jordan canonical form of J.

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