Functional (mathematics)

Functional (mathematics)

In mathematics, and particularly in functional analysis, a functional is a map from a vector space into its underlying scalar field. In other words, it is a function that takes a vector as its input argument, and returns a scalar. Commonly the vector space is a space of functions, thus the functional takes a function for its input argument, then it is sometimes considered a function of a function. Its use originates in the calculus of variations where one searches for a function that minimizes a certain functional. A particularly important application in physics is searching for a state of a system that minimizes the energy functional.

Transformations of functions is a rather more general concept, see Operator (mathematics).

Read more about Functional (mathematics):  Functional Equation, Functional Derivative and Functional Integration

Other articles related to "functional, functionals":

Functional (mathematics) - Functional Derivative and Functional Integration
... Functionalderivatives are used in Lagrangian mechanics ... They are derivatives of functionalsi.e ... they carry information on how a functionalchanges, when the function changes by a small amount ...

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