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corrected some pages
Several small mistakes/errors were corrected in several proofs/definitions.
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P/mvn-matn.md

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@@ -19,7 +19,7 @@ sources:
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title: "Matrix normal distribution"
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in: "Wikipedia, the free encyclopedia"
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pages: "retrieved on 2022-07-31"
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url: "https://en.wikipedia.org/wiki/Matrix_normal_distribution"
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url: "https://en.wikipedia.org/wiki/Matrix_normal_distribution#Definition"
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proof_id: "P330"
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shortcut: "mvn-matn"
@@ -38,7 +38,7 @@ $$
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Setting $p = 1$, $X = x$, $M = \mu$, $U = \Sigma$ and $V = 1$, we obtain
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$$ \label{eq:exp-pdf}
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$$ \label{eq:mvn-pdf}
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\begin{split}
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\mathcal{MN}(x; \mu, \Sigma, 1) &= \frac{1}{\sqrt{(2\pi)^{n} |1|^n |\Sigma|^1}} \cdot \exp\left[-\frac{1}{2} \mathrm{tr}\left( 1^{-1} (x-\mu)^\mathrm{T} \, \Sigma^{-1} (x-\mu) \right) \right] \\
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&= \frac{1}{\sqrt{(2\pi)^{n} |\Sigma|}} \cdot \exp\left[-\frac{1}{2} (x-\mu)^\mathrm{T} \, \Sigma^{-1} (x-\mu) \right]

P/norm-mvn.md

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@@ -11,7 +11,7 @@ title: "Normal distribution is a special case of multivariate normal distributio
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chapter: "Probability Distributions"
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section: "Univariate continuous distributions"
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topic: "Normal distribution"
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theorem: "Special case of matrix-normal distribution"
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theorem: "Special case of multivariate normal distribution"
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sources:
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- authors: "Wikipedia"

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