Point equation of the boundary of the numerical range of a matrix polynomial

Chien, MT; Nakazato, H; Psarrakos, P

dc.contributor.author	Chien, MT	en
dc.contributor.author	Nakazato, H	en
dc.contributor.author	Psarrakos, P	en
dc.date.accessioned	2014-03-01T01:18:13Z
dc.date.available	2014-03-01T01:18:13Z
dc.date.issued	2002	en
dc.identifier.issn	0024-3795	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14871
dc.subject	matrix polynomial	en
dc.subject	numerical range	en
dc.subject	boundary	en
dc.subject	discriminant	en
dc.subject.classification	Mathematics, Applied	en
dc.title	Point equation of the boundary of the numerical range of a matrix polynomial	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0024-3795(01)00549-3	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0024-3795(01)00549-3	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	The numerical range of an n x n matrix polynomial P(lambda) = A(m)lambda(m) + A(m-1)lambda(m-1) + .... + A(1)lambda + A(0) is defined by W(P) = {lambda is an element of C : x * P (lambda)x = 0, x is an element of C-n, x not equal 0}. For the linear pencil P(lambda) = Ilambda - A, the range W(P) coincides with the numerical range of matrix A, F(A) = {xAx: x is an element of C-n, xx = 1}. In this paper, we obtain necessary conditions for the origin to be a boundary point of F(A). As a consequence, an algebraic curve of degree at most 2n(n - 1)m, which contains the boundary of W(P), is constructed. (C) 2002 Elsevier Science Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	LINEAR ALGEBRA AND ITS APPLICATIONS	en
dc.identifier.doi	10.1016/S0024-3795(01)00549-3	en
dc.identifier.isi	ISI:000175670100013	en
dc.identifier.volume	347	en
dc.identifier.spage	205	en
dc.identifier.epage	217	en