# Definition:Positive Definite Matrix

## Definition

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

$\mathbf A$ is positive definite if and only if:

$(1): \quad \mathbf A$ 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.