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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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    https://brainmass.com/math/vector-calculus/complex-inner-products-orthonormal-sets-64778

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    Let be the vector space of all complex valued polynomials defined over ...

    Solution Summary

    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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