Cesaro limits of analytically perturbed stochastic matrices

Some Results on Polynomial Numerical Hulls of Perturbed Matrices

In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.

Perturbed Spectra of Defective Matrices

This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrix A is changed to A+ tE, where E = 0 and t > 0 is a small parameter. In particular, we analyse the rational exponents that may occur when the matrix E varies over the sphere ‖E‖ = ρ > 0. We partially characterize the leading exponents noting that t...

Eigensolutions of perturbed nearly defective matrices

Persistently positive inverses of perturbed M-matrices

A well known property of anM-matrixA is that the inverse is element-wise non-negative, which we write asA−1 0. In this paper we consider perturbations ofM-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The bounds are written in terms of decay estimates which characterize the decay (along rows) of the elements of the inverse matrix. We obtain results f...

Bounds on determinants of perturbed diagonal matrices

We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix. The matrices considered are, in general, diagonally dominant. The lower bounds are best possible, and in several cases they are stronger than well-known bounds due to Ostrowski and other authors. If A = I−E is a real n×n matrix and the e...