Positive definite function

In mathematics, the term positive-definite function may refer to a couple of different concepts.

A real-valued, continuously differentiable function f is positive definite on a neighborhood of the origin, D, if ${\displaystyle f(0)=0}$ and ${\displaystyle f(x)>0}$ for every non-zero ${\displaystyle x\in D}$. This definition is in clear conflict with the one below.

A positive-definite function of a real variable x is a complex-valued function f:R → C such that for any real numbers x₁, ..., x_n the n×n matrix

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