Exercise 6.1.12

Answers

Compute that

∥ \sum_{i = 1}^{k} a_{i} v_{i} ∥^{2} = ⟨ \sum_{i = 1}^{k} a_{i} v_{i} ⟩

= \sum_{i = 1}^{k} ∥ a_{i} v_{i} ∥^{2} + \sum_{i, j} ⟨ a_{i} v_{i}, a_{j} v_{j} ⟩

= \sum_{i = 1}^{k} | a_{i} |^{2} ∥ v_{i} ∥ .

jephianlin

2011-06-27 00:00