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单词 LinearFunctional
释义

linear functional


Let V be a vector spaceMathworldPlanetmath over a field K.A linear functionalMathworldPlanetmathPlanetmathPlanetmath (or linear form) on Vis a linear mapping ϕ:VK,where K is thought of as a one-dimensional vector space over itself.

The collectionMathworldPlanetmath of all linear functionals on Vcan be made into a vector spaceby defining additionPlanetmathPlanetmath and scalar multiplication pointwise;this vector space is called the dual spaceMathworldPlanetmathPlanetmathPlanetmath of V.

The term linear functional derives fromthe case where V is a space of functions(see the entry on functionalsMathworldPlanetmathPlanetmath (http://planetmath.org/Functional)).Some authors restrict the term to this case.

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