# Tagged Questions

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### Distributions of eigenvalues for matrix normal distribution: related references

I am interested in the distribution of the eigenvalues of matrices that are sampled from the matrix normal distribution. I am sampling from $p(X \mid M,U,V)$ and let's assume that I know the ...
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### Is Rellich's function valued theorem valid for a rank defficient function valued matrix?

Theorem (Rellich). Let $\boldsymbol{A}(t) : \mathbb{R}\rightarrow\mathbb{C}^{n \times n}$ be a Hermitian matrix function that depends on $t$ analytically. (i) The $n$ roots of the characteristic ...
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### Separating the spectrum of a Hermitian matrix

Given Hermitian matrix $A$, I would like to perturbate it so that its eigenvalues become well-separated. Specifically, let $A$ be some Hermitian matrix, and let $G$ be a Gaussian matrix, with each ...
Consider a matrix function $A(x)$, analytically depending on single parameter $x$. Consider the eigenvalue/eigenvector pair of $A(0)$, namely $\lambda(0)$ and $w(0)$. The question is whether we can ...