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