Exercise 6.A.19

Answers

Proof. We have

\begin{aligned} | | u + v | |^{2} - | | u - v | |^{2} & = ⟨ u + v, u + v ⟩ - ⟨ u - v, u - v ⟩ \\ = ⟨ u, u ⟩ + 2 ⟨ u, v ⟩ + ⟨ v, v ⟩ - (⟨ u, u ⟩ - 2 ⟨ u, v ⟩ + ⟨ v, v ⟩) \\ = 4 ⟨ u, v ⟩ \end{aligned}

Dividing by $4$ yields the desired result. □

celiopassos

2017-10-06 00:00