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由 Trivial 於 星期日 八月 13, 2006 11:20 pm
This is a basic fact of inner product space.#ed_op#BR#ed_cl#Take an orthonormal basis of V, (e_1,...,e_n)#ed_op#BR#ed_cl#Let F(e_i) = a_i, and take y = a_1e_1+...+a_ne_n#ed_op#BR#ed_cl#By checking,#ed_op#BR#ed_cl#F(e_i) = <e_i, y> because the basis is orthonormal#ed_op#BR#ed_cl#so we are done#ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
[問題]線代問題...希望高手可以幫忙..謝謝
由 cloudsea 於 星期四 四月 20, 2006 7:56 pm
#ed_op#DIV#ed_cl#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..#ed_op#/DIV#ed_cl#