(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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).

2. Relevant equations

Cayley-Hamilton Theorem?

3. 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 im even leading into the right direction. Any help on getting going with this proof?

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# Homework Help: Invariant Subspaces

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