Question

Let TEL(V) , and let PEPF) be a polynomial. Show that if \lambda is an eigenvalue of T, then p(\lambda) is an eigenvalue of p(T).

Hint: this follows from the more precise statement that if v \in V is a non-zero eigenvector for T for the eigenvalue \lambda, then v is also an eigenvector for p(T) for the eigenvalue p(\lambda). Prove this.

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Answer #1

and PEP (f) be a cost o out a let TELCV) polynomial. To share that ist is eigenvalue of T, then P (d) is eigenvalue of PCD).le proi)=a Color Thus dari is the desired eigenvalue =) p (2, ) is eigenvalue of P (T) P() is eigenvalue of PGT) Hence proof

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