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Questions tagged [matrix-normal]

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Prove that the joint density of independent multivariate normal variables is a matrix-normal

Let $X_1,...,X_n \sim N_p(\mu_i,\Sigma_i)$ be Multivariate Normal a.v. independent. Show that $W = (X_1,...,X_n) \sim MN(M,\mathbb{I},\Sigma)$ where $M = [\mu_1 \mu_2...\mu_n]$ and $\mathbb{I}$ ...
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SVD of a matrix normal: practical applications?

What are some practical applications of the distributions of the components of an SVD of a matrix of normals? In particular, assume $Y \sim N_{n \times p}({\bf 0}, \Sigma \otimes I)$, i.e. the rows ...
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Minimax equivalence of Matrix Norm

In a proof of random matrix theory, the author makes use of the following equivalence: \begin{equation} \inf_{v\in V(r)}\lVert Xv \rVert_2 = \inf_{v\in V(r)} \sup_{u \in S^{n-1}}u^TXv \end{equation} ...
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Find the derivative w.r.t. matrix normal distribution pdf

We have the pdf of matrix normal distribution for the random matrix $X$ (https://en.wikipedia.org/wiki/Matrix_normal_distribution): However here in my case, $X$ is of a parameter, say $\theta$. So my ...