On the q-numerical range of matrices and matrix polynomials

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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: y*P(lambda)x = 0, x, y is an element of C-n, x*x = 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

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