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 Space

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Linear Functional." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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