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Vector Spaces of Complex Valued Polynomials, Complex Inner Products and Orthonormal Sets

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Let V be the vector space of all complex valued polynomials defined over the half line [0,infinity).

(a) Show that <f,g> = &#8747; 0-->&#8734; 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.

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Vector Spaces of Complex Valued Polynomials, Complex Inner Products and Orthonormal Sets are investigated. The solution is detailed and well presented.

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