Linear Functional
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(alphav)=alphaT(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.
See also
Dual Vector Space, Functional, Generalized Function, Linear Function, Vector SpaceThis entry contributed by Todd Rowland
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Rowland, Todd. "Linear Functional." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LinearFunctional.html