linear functional

Let $V$ be a vector space over a field $K$ .A linear functional (or linear form) on $V$ is a linear mapping $\\phi\\colon V\\to K$ ,where $K$ is thought of as a one-dimensional vector space over itself.

The collection of all linear functionals on $V$ can be made into a vector spaceby defining addition and scalar multiplication pointwise;this vector space is called the dual space of $V$ .

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

单词	LinearFunctional
释义	linear functional Let $V$ be a vector space over a field $K$ .A linear functional (or linear form) on $V$ is a linear mapping $\\phi\\colon V\\to K$ ,where $K$ is thought of as a one-dimensional vector space over itself. The collection of all linear functionals on $V$ can be made into a vector spaceby defining addition and scalar multiplication pointwise;this vector space is called the dual space of $V$ . The term linear functional derives fromthe case where $V$ is a space of functions(see the entry on functionals (http://planetmath.org/Functional)).Some authors restrict the term to this case.
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