Failing at projection question

[reha]

let pf(x)= sum( from i=1 to k) <x, ui>ui, show pf is a projection.

Ive tried to show this fact myself but i failed. Please some one help me out. thanks

Note ui = u1...un an orthogonal basis of V where V is a vector space.

 

[Pere Callahan]

Welcome to PF, reha.

The usual procedure in showing that a given function is a projection, is to verify that is satisfies the definition of a projection. (By the way, that's true for many other things as well.)

So, what's the definition of a projection in a vector space?