Related papers: A note on variance bounds and location of eigenval…

We show that various old and new bounds involving eigenvalues of a complex n x n matrix are immediate consequences of the inequalities involving variance of real and complex numbers.

We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the…

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…

In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.

We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex…

We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.

Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example,…

We find sharp upper bounds for the multiplicities and the numerical values of all the distinct eigenvalues on a surface of revolution diffeomorphic to the sphere.

We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…

The purpose of this note is twofold: firstly to improve the known results on variation of extreme eigenvalues of birth and death matrices and random walk matrices; and secondly to progress towards the solution of a thirty years old open…

For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of $k$-regular…

We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…

This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…

A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.

We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues.

For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…

In this paper, we find bounds for the eigenvalues of matrix polynomials. In particular, we find generalizations of Cauchy's classical Theorem for distribution of eigenvalues of matrix polynomial.

We obtain bounds on the complex eigenvalues of non-self-adjoint Schr\"odinger operators with complex potentials, and also on the complex resonances of self-adjoint Schr\"odinger operators. Our bounds are compared with numerical results, and…

Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for…