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hitmeoff
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Homework Statement
Let T be a linear operator on a vector space V and let W be a T-Invariant subspace of V. Prove that W is g(T)-invariant for any polynomial g(t).
Homework Equations
Cayley-Hamilton Theorem?
The Attempt at a Solution
Im not sure how to begin. Ok so g(t) is the characteristic polynomial of T. If W is a T-Invariant subspace of V, then [tex]\forall[/tex]v[tex]\epsilon[/tex]W, T(v) [tex]\epsilon[/tex] W
So for any T with a characteristic polynomial g(t), W is still T-Invariant...not sure if I am even leading into the right direction. Any help on getting going with this proof?