All Questions

The Hermitian matrices form a real vector space where we have a Lebesgue measure. In the set of Hermitian matrices with Lebesgue measure, how does it follow that the set of Hermitian matrices with ...

Playing around with Matlab I noticed something very peculiar: Take the symmetric matrix $A \in \mathbb R^{n \times n}$ defined by $$A_{ij}= i \delta_{ij} - \frac{\varepsilon}{\sqrt{i}\sqrt{j}}\,.$$ ...

This is a follow up question on my previous question here that was on solved in the deterministic setting by Denis Serre, when the perturbation can be separated. Therefore, I decided to split the ...

Let $A\in\mathbb{R}^{n\times n}$ be a given normal matrix, i.e. $A^TA=AA^T$. Let $P_s\in\mathbb{R}^n$ be a random projection matrix to an $s$-dimensional subspace in $\mathbb{R}^n$. Suppose $\frac{A+...

Let $G_\mathbb{R}\in\mathbb{R}^{n\times n}$ and $G_\mathbb{C}\in\mathbb{C}^{n\times n}$ denote the real and complex Ginibre random matrices, i.e. random matrices with independent real/complex Gaussian ...

I would like to find the largest eigenvalue distribution of the following tridiagonal symmetric random matrix in an analytic way. All the ${\lambda}_i$ are distributed the same way with chi-square (...