Related papers: A Resolvent Criterion for Normality

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

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 consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…

We study the spectral norm of matrices M that can be factored as M=BA, where A is a random matrix with independent mean zero entries, and B is a fixed matrix. Under the (4+epsilon)-th moment assumption on the entries of A, we show that the…

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

A.A. Suslin proved a normality theorem for an elementary linear group, which says that an elementary linear group of size bigger than or equal to 3 over a commutative ring with unity is normal in the general linear group of same size.…

A stratified pseudomanifold is normal if its links are connected. A normalization of a stratified pseudomanifold $X$ is a normal stratified pseudomanifold $Y$ together with a finite-to-one projection $n:Y\to X$ satisfying a local condition…

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…

We provide a sufficient condition for solvability of a system of real quadratic equations $p_i(x)=y_i$, $i=1, \ldots, m$, where $p_i: {\mathbb R}^n \longrightarrow {\mathbb R}$ are quadratic forms. By solving a positive semidefinite…

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let $\Gamma$ be a graph with vertex set $V$, diameter $D$, adjacency matrix $A$, and…

Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in…

We derive, similar to Lau and Riha, a matrix formulation of a general best approximation theorem of Singer for the special case of spectral approximations of a given matrix from a given subspace. Using our matrix formulation we describe the…

In this paper we generalize a result of Ye, Pang and Yang[12] on the normality of a family of holomorphic curves in $P^N(\mathbb{C})$. Further we obtain a normality criterion for family of meromorphic functions that partially share…

We characterize the infimum of a matrix norm of a square matrix A induced by an absolute norm, over the fields of real and complex numbers. Usually this infimum is greater than the spectral radius of A. If A is sign equivalent to a…

Let $X$ be a matrix sampled uniformly from the set of doubly stochastic matrices of size $n\times n$. We show that the empirical spectral distribution of the normalized matrix $\sqrt{n}(X-{\mathbf {E}}X)$ converges almost surely to the…

A symmetric doubly stochastic matrix A is said to be determined by its spectra if the only symmetric doubly stochastic matrices that are similar to A are of the form $P^TAP$ for some permutation matrix P. The problem of characterizing such…

A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra $SH$ is recovered from modules over a commutative…

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…

In this work the spectral theory of self-adjoint operator $A$ represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of $A$. Different criteria of absolute…

Let $B$ and $C$ be square complex matrices. The differential equation \begin{equation*} x''(t)+Bx'(t)+Cx(t)=f(t) \end{equation*} is considered. A solvent is a matrix solution $X$ of the equation $X^2+BX+C=\mathbf0$. A pair of solvents $X$…