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#