**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

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### Famous quotes containing the word functional:

“Indigenous to Minnesota, and almost completely ignored by its people, are the stark, unornamented, *functional* clusters of concrete—Minnesota’s grain elevators. These may be said to express unconsciously all the principles of modernism, being built for use only, with little regard for the tenets of esthetic design.”

—Federal Writers’ Project Of The Wor, U.S. public relief program (1935-1943)