This is given as a sample exercise for our final exam in our Numerical Analysis class. However, nowhere in the course has the notion of approximant been defined or how to approach this kind of problem . What I found on the web doesn't really seem compatible with this problem.
Let $g^* \in G$ represent the best approximant for $f \in F$, such that $<f-g,g^*> = 0 , \forall g \in G $
Prove that $g^*$ is unique.
Can anyone point the way to a solution ? If you don't have the time, I would also appreciate some references.