Let $\Sigma \in \mathbb{R}^{N \times N}$ be a
D4571: Real matrix such that
| (i) |
\begin{equation}
\text{det} \Sigma
\neq 0
\end{equation}
|
| (ii) |
\begin{equation}
\Sigma^T
= \Sigma
\end{equation}
|
| (iii) |
$\Sigma^{-1}$ is an D2089: Inverse matrix for $\Sigma$
|
The
euclidean real gaussian density function on $\mathbb{R}^{N \times 1}$
with parameters $\mu \in \mathbb{R}^{N \times 1}$ and $\Sigma$ is the
D4364: Real function
\begin{equation}
\mathbb{R}^{N \times 1} \to \mathbb{R}, \quad
x \mapsto \frac{1}{\sqrt{(2 \pi)^n \text{det} \Sigma}} \exp \left( - \frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right)
\end{equation}
