functional
Definition
A functional $T$ is a function mapping a function space (often a vector space^{}) $V$ in to a field of scalars $K$, typically taken to be $\mathbb{R}$ or $\u2102$.
Discussion
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 functionals^{} are those functionals $T$ that

•
$T(x+y)=T(x)+T(y)$

•
$T(cx)=cT(x)$
for any $c\in K$, $x,y\in V$.
Title  functional 

Canonical name  Functional 
Date of creation  20130322 12:29:45 
Last modified on  20130322 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 