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Definition D2718
Euclidean real gaussian density function

Let $\Sigma \in \mathbb{R}^{N \times N}$ be a D4571: Real matrix such that
 (i) $$\text{det} \Sigma \neq 0$$ (ii) $$\Sigma^T = \Sigma$$ (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 $$\mathbb{R}^{N \times 1} \to \mathbb{R}, \quad x \mapsto \frac{1}{\sqrt{(2 \pi)^n \text{det} \Sigma}} \exp \left( - \frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right)$$
Children
 ▶ Standard euclidean real gaussian density function