A linear functional on a real vector space V is a function T:V->R, which satisfies the following properties. 1.T(v + w) = T(v) + T(w), and 2.T(α v) = α T(v). When V is a complex vector space, then T is a linear map into the complex numbers. Generalized functions are a special case of linear functionals, and have a rich theory surrounding them.
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