.Prove that:

( = orthogonal complement)

Attempt at solution:

Let and

Then

Make sure here to write , and remark you're using additivity of the inner product

Therefore

As above, write , and don't write u,w

below: it's enough you already remarked that

Tonio

Let and and

Then

Therfore,

Is this okay or is it totally wrong? Please help. Thanks alot in advance.