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Exercise 5.B.16

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Proof. Let $n = \dim V$ . Define $Ψ \in L (P_{n} (ℂ), V)$ by

Ψ (p) = (p (T)) v

for $p \in P_{n} (ℂ)$ . One can easily verify that $Ψ$ is linear. Since $\dim P_{n} (ℂ) > \dim V$ , by 3.23, there exists $p \in P_{n} (ℂ)$ such that $0 = Ψ (p) = (p (T)) v$ . The rest follows exactly as 5.21. □

celiopassos

2017-10-06 00:00

Exercise 5.B.16

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