YLL討論網

cloudsea · 由 **cloudsea** 於星期四四月 20, 2006 7:56 pm

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..

Trivial · 由 **Trivial** 於星期日八月 13, 2006 11:20 pm

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

YLL討論網

[問題]線代問題...希望高手可以幫忙..謝謝

[問題]線代問題...希望高手可以幫忙..謝謝