On the q-numerical range of matrices and matrix polynomials

Chien, M-T; Nakazato, H; Psarrakos, P

dc.contributor.author	Chien, M-T	en
dc.contributor.author	Nakazato, H	en
dc.contributor.author	Psarrakos, P	en
dc.date.accessioned	2014-03-01T11:44:40Z
dc.date.available	2014-03-01T11:44:40Z
dc.date.issued	2005	en
dc.identifier.issn	0308-1087	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/37083
dc.subject	Boundary	en
dc.subject	Connectedness	en
dc.subject	Eigenvalue	en
dc.subject	Ellipse	en
dc.subject	Local dimension	en
dc.subject	Matrix polynomial	en
dc.subject	q-numerical range	en
dc.subject.classification	Mathematics	en
dc.subject.other	BOUNDARY	en
dc.title	On the q-numerical range of matrices and matrix polynomials	en
heal.type	other	en
heal.identifier.primary	10.1080/03081080500167596	en
heal.identifier.secondary	http://dx.doi.org/10.1080/03081080500167596	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	The q-numerical range (0 <= q <= 1) of an n x n matrix polynomial P(lambda) = A(m)lambda(m)+center dot center dot center dot+ A(1)lambda + A(0) is defined by W-q(P) = {lambda is an element of C: yP(lambda)x = 0, x, y is an element of C-n, xx = y* y = 1, y* x = q}. In this article, we investigate the boundary and the shape of W-q(P), using the notion of local dimension. We also obtain that the q-numerical range of first-order matrix polynomials is always simply connected. Moreover, the special cases of 2 x 2 matrices and matrix polynomials are considered. In particular, the boundary of the q-numerical range of a 2 x 2 matrix polynomial of degree m lies on an algebraic curve of degree at most 8m.	en
heal.publisher	TAYLOR & FRANCIS LTD	en
heal.journalName	Linear and Multilinear Algebra	en
dc.identifier.doi	10.1080/03081080500167596	en
dc.identifier.isi	ISI:000231535800004	en
dc.identifier.volume	53	en
dc.identifier.issue	5	en
dc.identifier.spage	357	en
dc.identifier.epage	374	en