Exercise 6.1.9

Answers

1.

Represent

x

to be a linear combination of

β

x = \sum_{i = 1}^{k} a_{i} z_{i},

where $z_{i}$ ’s are elements in $β$ . Then we have

⟨ x, x ⟩ = ⟨ x, \sum_{i = 1}^{k} a_{i} z_{i} ⟩

= \sum_{i = 1}^{k} \bar{a_{i}} ⟨ x, z_{i} ⟩ = 0

and so $x = 0$ .

2.

This means that

⟨ x - y, z ⟩ = 0

for all

z \in β

. So we have

x - y = 0

and

x = y

jephianlin

2011-06-27 00:00