Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/98595
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorLau, PSen_US
dc.creatorLi, CKen_US
dc.creatorPoon, YTen_US
dc.creatorSze, NSen_US
dc.date.accessioned2023-05-10T02:00:33Z-
dc.date.available2023-05-10T02:00:33Z-
dc.identifier.issn0024-3795en_US
dc.identifier.urihttp://hdl.handle.net/10397/98595-
dc.language.isoenen_US
dc.publisherElsevier Inc.en_US
dc.rights© 2018 Elsevier Inc. All rights reserved.en_US
dc.rights© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/.en_US
dc.rightsThe following publication Lau, P. S., Li, C. K., Poon, Y. T., & Sze, N. S. (2019). The generalized numerical range of a set of matrices. Linear Algebra and its Applications, 563, 24-46 is available at https://doi.org/10.1016/j.laa.2018.09.023.en_US
dc.subjectNumerical rangeen_US
dc.subjectConvex seten_US
dc.subjectStar-shaped seten_US
dc.titleThe generalized numerical range of a set of matricesen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage24en_US
dc.identifier.epage46en_US
dc.identifier.volume563en_US
dc.identifier.doi10.1016/j.laa.2018.09.023en_US
dcterms.abstractFor a given set of n×n matrices F, we study the union of the C-numerical ranges of the matrices in the set F, denoted by WC(F). We obtain basic algebraic and topological properties of WC(F), and show that there are connections between the geometric properties of WC(F) and the algebraic properties of C and the matrices in F. Furthermore, we consider the starshapedness and convexity of the set WC(F). In particular, we show that if F is the convex hull of two matrices such that WC(A) and WC(B) are convex, then the set WC(F) is star-shaped. We also investigate the extensions of the results to the joint C-numerical range of an m-tuple of matrices.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationLinear algebra and its applications, 15 Feb. 2019, v. 563, p. 24-46en_US
dcterms.isPartOfLinear algebra and its applicationsen_US
dcterms.issued2019-02-15-
dc.identifier.scopus2-s2.0-85055259716-
dc.identifier.eissn1873-1856en_US
dc.description.validate202305 bcchen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumberAMA-0310-
dc.description.fundingSourceRGCen_US
dc.description.fundingSourceOthersen_US
dc.description.fundingTextPolyUen_US
dc.description.pubStatusPublisheden_US
dc.identifier.OPUS13006145-
dc.description.oaCategoryGreen (AAM)en_US
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