Assume that V is a finite dimensional vector space and T is in End(V ). Recall that

if p in K[x] is a polynomial, then we can define a new linear map p(T). Show

that if is an eigenvalue of T then p() is an eigenvalue of p(T).

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- February 6th 2008, 06:40 PMalexmineigenvectors and eigenvalues
Assume that V is a finite dimensional vector space and T is in End(V ). Recall that

if p in K[x] is a polynomial, then we can define a new linear map p(T). Show

that if is an eigenvalue of T then p() is an eigenvalue of p(T).