Exercise 5.B.10

Answers

Proof. Note that $T^{k} v = λ^{k} v$ . Let $n = \deg p$ and $a_{0}, a_{1}, \dots, a_{n} \in 𝔽$ be the coefficients of $p$ . Then

\begin{aligned} p (T) v & = (\sum_{k = 0}^{n} a_{k} T^{k}) v \\ = \sum_{k = 0}^{n} a_{k} T^{k} v \\ = \sum_{k = 0}^{n} a_{k} λ^{k} v \\ = (\sum_{k = 0}^{n} a_{k} λ^{k}) v \\ = p (λ) v \end{aligned}

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celiopassos

2017-10-06 00:00