Exercise 6.A.4

Answers

Proof. (a) We have

\begin{aligned} ⟨ u + v, u - v ⟩ & = ⟨ u, u ⟩ - ⟨ u, v ⟩ + ⟨ v, u ⟩ - ⟨ v, v ⟩ \\ = ⟨ u, u ⟩ - ⟨ v, v ⟩ \\ = | | u | |^{2} - | | v^{2} | | \end{aligned}

(b) This follows directly from the above.

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2017-10-06 00:00