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?