I've attached a picture with the problem statement. I've done some least squares problems with matrices, but I don't think that will work here.

I thought I'd just find the orthogonal projection of f(x) onto W directly, but in order to do that I need basis vectors for W.

I don't really understand what the vector space W is here. Is it a subspace of V, where V is all continuous functions with a function value between -pi and pi? Or is it the input in e^ix which is between -pi and pi?

If I could get some help clarifying that vector space notation, I believe I will be able to solve the problem.

Thanks!