本帖最后由 厚积薄发 于 2010-1-26 21:12 编辑 3 z3 J- A" Z2 x$ ^7 w5 ]% `( x0 _' E) U( x
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.8 x: z: W6 ^$ |) o2 s5 y4 o) ~* v) w
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. 4 e, c7 i0 k! k$ D* zTransformations of functions is a somewhat more general concept, see operator.