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 $ℝ$ or $ℂ$.

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 $c\in K$, $x,y\in V$.