Question:
Vector Spaces of Complex Valued Polynomials, Complex Inner Products and Orthonormal Sets
Let V be the vector space of all complex valued polynomials defined over the half line [0,infinity).
(a) Show that = ∫ 0-->∞ f(x) ( g(x) bar) e^-x dx is a complex inner product on V g(x) bar is g(x) with a bar on it, which I believe to be the conjugate.
(b) Find an orthonormal set : {f_o, f_1} in V such that span{e_o,e_1} = span{f_o,f_1}, where e_o(x) = 1 and e_i(x) = x.