# Definition:Positive Definite Functional

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 It has been suggested that this page or section be renamed: Positive Definite Real-Valued Functional, to be more precise One may discuss this suggestion on the talk page.

## Definition

Let $f : S \to T$ be a mapping.

Let $f \in \MM$, where $\MM$ stands for some function space.

Let $F \sqbrk f : \MM \to \R$ be a real-valued functional.

Suppose:

$\forall f \in \MM: F \sqbrk f > 0$

Then $F$ is a positive-definite functional.