A primer of Perron-Frobenius theory for matrix polynomials

Psarrakos, PJ; Tsatsomeros, MJ

dc.contributor.author	Psarrakos, PJ	en
dc.contributor.author	Tsatsomeros, MJ	en
dc.date.accessioned	2014-03-01T01:19:47Z
dc.date.available	2014-03-01T01:19:47Z
dc.date.issued	2004	en
dc.identifier.issn	0024-3795	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15713
dc.subject	Matrix polynomial	en
dc.subject	Multistep difference equation	en
dc.subject	Nonnegative matrix	en
dc.subject	Numerical range	en
dc.subject	Perron polynomial	en
dc.subject	Perron-Frobenius	en
dc.subject	Spectral radius	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Difference equations	en
dc.subject.other	Linearization	en
dc.subject.other	Mathematical operators	en
dc.subject.other	Optimization	en
dc.subject.other	Polynomials	en
dc.subject.other	Random processes	en
dc.subject.other	Theorem proving	en
dc.subject.other	Matrix polynomials	en
dc.subject.other	Multistep difference equation	en
dc.subject.other	Nonnegative matrix	en
dc.subject.other	Numerical range	en
dc.subject.other	Perron polynomial	en
dc.subject.other	Spectral radius	en
dc.subject.other	Matrix algebra	en
dc.title	A primer of Perron-Frobenius theory for matrix polynomials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.laa.2003.12.026	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.laa.2003.12.026	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	We present an extension of Perron-Frobenius theory to the spectra and numerical ranges of Perron polynomials, namely, matrix polynomials of the form L(lambda) = Ilambda(m) -A(m-1)lambda(m-1) - (...) - A(1)lambda - A(0), where the coefficient matrices are entrywise nonnegative. Our approach relies on the companion matrix linearization. First, we recount the generalization of the Perron-Frobenius Theorem to Perron polynomials and report some of its consequences. Subsequently, we examine the role of L(lambda) in multistep difference equations and provide a multistep version of the Fundamental Theorem of Demography. Finally, we extend Issos' results on the numerical range of nonnegative matrices to Perron polynomials. (C) 2004 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Linear Algebra and Its Applications	en
dc.identifier.doi	10.1016/j.laa.2003.12.026	en
dc.identifier.isi	ISI:000224949200023	en
dc.identifier.volume	393	en
dc.identifier.issue	1-3	en
dc.identifier.spage	333	en
dc.identifier.epage	351	en