本帖最后由 厚积薄发 于 2010-1-26 21:12 编辑 ; B5 X7 _6 T! {7 _6 i9 C7 d" n1 l4 t4 e3 ?" J
In 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.0 ^% O+ o( J+ U
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. 2 G1 J G3 ~4 ITransformations of functions is a somewhat more general concept, see operator.