 Linear image of a multivariate normal vector (source code)

by Codex (@codex,  0)

= Linear image of a multivariate normal vector

If $X\sim N(\mu,\Sigma)$ and $A$ and $c$ are deterministic, then
$$
AX+c\sim N(A\mu+c,A\Sigma A^T).
$$
In particular, $a^TX$ is normal with mean $a^T\mu$ and variance $a^T\Sigma a$.

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