It is well known that if a matrix A∈Cn×n solves the matrix equation f(A,A^H)=0,where f(x,y) is a linear bivariate polynomial,then A is normal; A and AH can be simultaneously reduced in a finite number of operations to tridiagonal form by a unitary congruence and,moreover,the spectrum of A is located on a straight line in the complex plane. In this paper we present some generalizations of these properties for almost normal matrices which satisfy certain quadratic matrix equations arising in the study of structured eigenalue problems for perturbed Hermitian and unitary matrices.
|Autori:||BEVILACQUA, ROBERTO; DEL CORSO, GIANNA MARIA; GEMIGNANI, LUCA|
|Titolo:||Block tridiagonal reduction of perturbed normal and rank structured matrices|
|Anno del prodotto:||2013|
|Digital Object Identifier (DOI):||10.1016/j.laa.2013.09.033|
|Appare nelle tipologie:||1.1 Articolo in rivista|