# Definition:Positive Definite (Ring)

## Definition

Let $\struct {R, +, \times}$ be a ring whose zero is denoted $0_R$.

Let $f: R \to \R$ be a (real-valued) function on $R$.

Then $f$ is positive definite if and only if:

$\forall x \in R: \begin {cases} \map f x = 0 & : x = 0_R \\ \map f x > 0 & : x \ne 0_R \end {cases}$