Definite triples of Hermitian matrices and matrix polynomials

Psarrakos, PJ

dc.contributor.author	Psarrakos, PJ	en
dc.date.accessioned	2014-03-01T01:18:48Z
dc.date.available	2014-03-01T01:18:48Z
dc.date.issued	2003	en
dc.identifier.issn	0377-0427	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15214
dc.subject	Crawford number	en
dc.subject	Gyroscopic system	en
dc.subject	Joint inner numerical radius	en
dc.subject	Joint numerical range	en
dc.subject	Matrix polynomial	en
dc.subject	Quasihyperbolic polynomial	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Definite triples	en
dc.subject.other	Hermitian matrices	en
dc.subject.other	Polynomials	en
dc.subject.other	mathematical analysis	en
dc.title	Definite triples of Hermitian matrices and matrix polynomials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0377-0427(02)00736-7	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0377-0427(02)00736-7	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	Let A, B and C be three n x. n nonzero Hermitian matrices. The triple (A, B, C) is called definite if the convex hull of the joint numerical range F(A,B, C)= {(xAx,xBx,xCx) is an element of R-3: x is an element of C-n,xx=1} does not contain (0, 0, 0). If the triple (A, B, C) is nondefinite, then the numerical ranges of the matrix polynomials Q(A) = Alambda(nu3) +Blambda(nu2) + Clambda(nu1) (nu(3) > nu(2) > nu(1) greater than or equal to 0) and L(lambda) = Alambda(zeta2) + (B + i C)lambda(zeta1) (zeta(2) > 1 greater than or equal to 0) coincide with the whole complex plane, providing no information. As a consequence, it is of particular interest to characterize a definite triple (A, B, C) and find the distance between (0, 0, 0) and the boundary of F(A, B, C). The distance between a nondefinite triple (A, B ,C) and the "nearest" definite triples with specified properties is also investigated. Moreover, applications of definite triples on matrix polynomials of special interest are presented. (C) 2002 Elsevier Science B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Computational and Applied Mathematics	en
dc.identifier.doi	10.1016/S0377-0427(02)00736-7	en
dc.identifier.isi	ISI:000180362500004	en
dc.identifier.volume	151	en
dc.identifier.issue	1	en
dc.identifier.spage	39	en
dc.identifier.epage	58	en