" I% e4 k: K6 CIn mathematics, a functional is traditionally a map from a vector space to the field underlying the vector space, which is usually the real numbers. In other words, it is a function that takes a vector as its argument or input and returns a scalar. Its use goes back to the calculus of variations where one searches for a function which minimizes a certain functional. A particularly important application in physics is to search for a state of a system which minimizes the energy functional./ D% j4 S& P* J, E1 @6 `
In functional analysis, the functional is also used in a broader sense as a mapping from an arbitrary vector space into the underlying scalar field (usually, real or complex numbers). A special kind of such functionals, linear functionals, gives rise to the study of dual spaces. 0 v+ @2 N7 ]- [3 F7 I% k2 Q8 [Transformations of functions is a somewhat more general concept, see operator.
