gaussian random vectors are closed under linear transformations

[[concept]]

Topics

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Theorem

Let $x\in {\mathbb{R}}^d\sim (\mu ,\Sigma )$ be a gaussian random vector, $A\in {\mathbb{R}}^{d^{\prime }\times d}$, and $b\in {\mathbb{R}}^{d^{\prime }}$. Then $Ax+b$ is also a gaussian random vector with $\text{Law}(Ax+b)=\mathcal{N}(A\mu +b,A\Sigma A^T)$ ie, gaussian random vectors are closed under linear transformations.

References

References

See Also

Mentions

Mentions

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