Related papers: Eigenvalue bounds for matrix polynomials in genera…

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.

In this paper, we establish bounds for the eigenvalues of matrix polynomials. Specifically, we find different generalizations of the Enestrom-Kakeya Theorem for matrix polynomials.

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.

This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue…

We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouch\'{e} theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of…

In this article we give bounds for the eigenvalues of a matrix, which can be seen as a common generalization of meet and join matrices and therefore also as a generalization of both GCD and LCM matrices. Although there are some results…

We show how $\ell$-ifications, which are companion forms of matrix polynomials, namely, lower order matrix polynomials with the same eigenvalues as a given complex square matrix polynomial, can be used in combination with other recent…

The standard approach for finding eigenvalues and eigenvectors of matrix polynomials starts by embedding the coefficients of the polynomial into a matrix pencil, known as linearization. Building on the pioneering work of Nakatsukasa and…

We study the average condition number for polynomial eigenvalues of collections of matrices drawn from various random matrix ensembles. In particular, we prove that polynomial eigenvalue problems defined by matrices with Gaussian entries…

We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.

It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2} < |\lambda| < 2$. We prove in this short note that under certain assumptions, matrix polynomials with either doubly…

Combined perturbation bounds are presented for eigenvalues and eigenspaces of Hermitian matrices or singular values and singular subspaces of general matrices. The bounds are derived based on the smooth decompositions and elementary…

We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…

We show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of nonnegative matrices.

Let ({\lambda}, v) be a known real eigenpair of a square real matrix A. In this paper it is shown how to locate the other eigenvalues of A in terms of the components of v. The obtained region is a union of Gershgorin discs of the second…

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…

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 study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices. We provide new bounds for generalized eigenvalues of meet matrices with respect to join matrices under very general…

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…

In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…