Related papers: The spectral spread of Hermitian matrices

We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical algebra adapted to ordered valued fields. We focus on the…

Let ${\mathcal S}_m$ be the set of all $m\times m$ density matrices (Hermitian positively semi-definite matrices of unit trace). Consider a problem of estimation of an unknown density matrix $\rho\in {\mathcal S}_m$ based on outcomes of $n$…

For a fixed quadratic polynomial $\mathfrak{p}$ in $n$ non-commuting variables, and $n$ independent $N\times N$ complex Ginibre matrices $X_1^N,\dots, X_n^N$, we establish the convergence of the empirical spectral distribution of $P^N…

This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random…

We establish a connection between quantum mechanics and computation, revealing fundamental limitations for algorithms computing spectra, especially in non-Hermitian settings. Introducing the concept of locally trivial pseudospectra (LTP),…

We study n by n symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most exp(-n^c), and the spectral norm of the inverse of H is O(sqrt{n}). Furthermore, the…

We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…

Identifying the spectrum of the sum of two given Hermitian matrices with fixed eigenvalues is the famous Horn's problem.In this note, we investigate a variant of Horn's problem, i.e., we identify the probability density function (abbr. pdf)…

We prove, under a certain representation theoretic assumption, that the set of real symmetric matrices, whose eigenvalues satisfy a linear matrix inequality, is itself a spectrahedron. The main application is that derivative relaxations of…

This text is about spiked models of non Hermitian random matrices. More specifically, we consider matrices of the type $A+P$, where the rank of $P$ stays bounded as the dimension goes to infinity and where the matrix $A$ is a non Hermitian…

The eigenvalues and eigenvectors of nonnormal matrices can be unstable under perturbations of their entries. This renders an obstacle to the analysis of numerical algorithms for non-Hermitian eigenvalue problems. A recent technique to…

In this paper, convergence rates of the spectral distributions of quaternion self-dual Hermitian matrices are investigated. We show that under conditions of finite 6th moments, the expected spectral distribution of a large quaternion…

A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

Let $r_A(T)$ denote the $A$-spectral radius of an operator $T$ which is bounded with respect to the seminorm induced by a positive operator $A$ on a complex Hilbert space $\mathcal{H}$. In this paper, we aim to establish some $A$-spectral…

Let $M_n$ be a class of symmetric sparse random matrices, with independent entries $M_{ij} = \delta_{ij} \xi_{ij}$ for $i \leq j$. $\delta_{ij}$ are i.i.d. Bernoulli random variables taking the value $1$ with probability $p \geq…

In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter $\beta>1$, of the basic Toeplitz matrix-sequence…

We consider Hermitian random band matrices $H$ in $d \geq 1 $ dimensions. The matrix elements $H_{xy},$ indexed by $x, y \in \Lambda \subset \mathbb{Z}^d,$ are independent, uniformly distributed random variable if $|x-y| $ is less than the…

We introduce a non-Hermitian $\beta$-ensemble and determine its spectral density in the limit of large $\beta$ and large matrix size $n$. The ensemble is given by a general tridiagonal complex random matrix of normal and chi-distributed…

In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…