\begin{definition}[Definition:Positive Definite Matrix]
Let $\mathbf A$ be a square matrix of order $n$.
$\mathbf A$ is '''positive definite''' {{iff}}:
:$(1): \quad \mathbf A$ is symmetric
:$(2): \quad$ for all column matrices $\mathbf x$ of order $n$, $\mathbf x^\intercal \mathbf A \mathbf x$ is strictly positive.
\end{definition}