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Exercise 5.B.12

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Proof. Define $T \in L (ℝ^{4})$ by

T (x_{1}, x_{2}, x_{3}, x_{4}) = (x_{2}, x_{3}, x_{4}, - x_{1})

Let $p \in P (R)$ such that $p (x) = x^{4}$ . Then $- 1$ is an eigenvalue of $p (T)$ , but $p$ is always positive, therefore no eigenvalue $λ$ of $T$ satisfies $p (λ) = - 1$ . □

celiopassos

2017-10-06 00:00

Exercise 5.B.12

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