A functional T is a function mapping a function space (often a vector spaceMathworldPlanetmath) V in to a field of scalars K, typically taken to be or .


Examples of functionals include the integral and entropy. A functional f is often indicated by the use of brackets, T[x] rather than T(x).

The linear functionalsMathworldPlanetmath are those functionals T that

  • T(x+y)=T(x)+T(y)

  • T(cx)=cT(x)

for any cK, x,yV.

Title functional
Canonical name Functional
Date of creation 2013-03-22 12:29:45
Last modified on 2013-03-22 12:29:45
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Definition
Classification msc 03E20
Defines linear functional