Let V be a finite-dimensional real inner product space with inner product < , >.
Let L:V->R be a linear map.
Show that there exists a vector u in V such that L(x) = <x,u> for all x in V.
2. The attempt at a solution
It seems really simple but I just can't phrase it properly.
I know since L is linear, I can express as L(x+y) = L(x) + L(y)
I tried to make x and u be expressed as combination of orthogonal basis, and try to work in the fact that inner product will result in ZERO since they are orthogonal.
Any help would be greatly appreciated.