Hi, I am having difficulty with the following proof:
Let V be an inner product space (real of dimension n) with two inner products in V, <,> and [,]. Prove that there exists a linear mapping on V such that [L(x),L(y)] = <x,y> for all x,y in V.
I am stuck as to where to go with the proof. I know that I need to construct a linear mapping with the above property, however I'm not sure where to go from there. Any insight into this would be appreciated.