Normal nonnegative realization of spectra

Autor:	Ana I. Julio, Ricardo Soto, Cristina B. Manzaneda
Rok vydání:	2014
Předmět:	Combinatorics Matrix (mathematics) Multilinear algebra Algebra and Number Theory Inverse Elementary divisors Nonnegative matrix Metzler matrix Complex number Eigenvalues and eigenvectors Mathematics
Zdroj:	Linear and Multilinear Algebra. 63:1204-1215
ISSN:	1563-5139 0308-1087
DOI:	10.1080/03081087.2014.924513
Popis:	The nonnegative inverse eigenvalue problem is the problem of finding necessary and sufficient conditions for the existence of an entrywise nonnegative matrix A with prescribed spectrum. This problem remains open for . If the matrix A is required to be normal, the problem will be called the normal nonnegative inverse eigenvalue problem (NNIEP). Sufficient conditions for a list of complex numbers to be the spectrum of a normal nonnegative matrix were obtained by Xu [Linear Multilinear Algebra. 1993;34:353–364]. In this paper, we give a normal version of a rank-r perturbation result due to Rado and published by Perfect [Duke Math. J. 1955;22:305–311], which allow us to obtain new sufficient conditions for the NNIEP to have a solution. These new conditions significantly improve Xu’s conditions. We also apply our results to construct nonnegative matrices with arbitrarily prescribed elementary divisors.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ee18cde4634a7ee2f2c5945ddef42de9 https://doi.org/10.1080/03081087.2014.924513 Zobrazit plný text záznamu