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T-invariant subspace

by gatekeeper
Tags: subspace, tinvariant
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gatekeeper
#1
Dec13-08, 10:49 AM
P: 1
Let the minimal polynomial of T on a finite dimensional vector space V be p where p is irreducible. Show that a cyclic submodule of V does not contain a proper T invariant subspace.

Let the minimal polynomial of T on a finite dimensional vector space V be p^2 where p is irreducible. Is it true that V contains a proper T invariant subspace?
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