Definition:Positive Definite Matrix

Definition
Let $\mathbf A$ be a square matrix of order $n$.

$\mathbf A$ is positive definite :
 * $(1): \quad \mathbf A$ is symmetric
 * $(2): \quad$ for all column matrices $\mathbf x$ of order $n$, $\mathbf x^\intercal \mathbf A \mathbf x$ is strictly positive.

Also known as
Some sources hyphenate: positive-definite.