A thm says: if W is a subspace of V then V = direct sum of W and CW( ort. complement of W) i.e. for all v € V there exist w € W & w' € CW s.t. v= w+w' Does it mean that we can write a function as a sum of two orthogonal funcs ? Also i don't know the proof for this thm ,Can you also send a simple sketch of proof ? Thanks..