Let ( V,<,>)be a finite-dimensional inner product space over C and F : V-->C be linear . Show that there exists an unique y∈V such that F(x) = <x,y> for all x∈ V 沒什麼想法......想令V為R^n..但又不能這樣想..因為這樣好像只是證其中一特例..
This is a basic fact of inner product space. Take an orthonormal basis of V, (e_1,...,e_n) Let F(e_i) = a_i, and take y = a_1e_1+...+a_ne_n By checking, F(e_i) = <e_i, y> because the basis is orthonormal so we are done