Question: Suppose T is a linear operator on a vector space V over a field F. Prove the following. (a) If A is an eigenvalue of

Suppose T is a linear operator on a vector space V over a field F. Prove the following. (a) If A is an eigenvalue of T and Ex is its eigenspace, then Ex is T-invariant. (b) If W is a T-invariant subspace of V, then W is g(T)-invariant for any polynomial g(t) with coefficients in F

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