Canonical forms for families of anti-commuting diagonalizable linear operators

dc.contributor.authorBilge, Ayşe Hümeyra
dc.contributor.authorBilge, Ayşe Hümeyra
dc.date.accessioned2019-06-27T08:04:33Z
dc.date.available2019-06-27T08:04:33Z
dc.date.issued2012
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.description.abstractIt is well known that a commuting family of diagonalizable linear operators on a finite dimensional vector space is simultaneously diagonalizable. In this paper we consider a family A = {A(a)} A(a) : V -> V a = 1... N of anti-commuting (complex) linear operators on a finite dimensional vector space. We prove that if the family is diagonalizable over the complex numbers then V has an A-invariant direct sum decomposition into subspaces V(alpha) such that the restriction of the family A to V(alpha) is a representation of a Clifford algebra. Thus unlike the families of commuting diagonalizable operators diagonalizable anti-commuting families cannot be simultaneously digonalized but on each subspace they can be put simultaneously to (non-unique) canonical forms. The construction of canonical forms for complex representations is straightforward while for the real representations it follows from the results of [A.H. Bilge S. Kocak S. Uguz Canonical bases for real representations of Clifford algebras Linear Algebra Appl. 419 (2006) 417-439]. (C) 2011 Elsevier Inc. All rights reserved.en_US]
dc.identifier.citation0
dc.identifier.doi10.1016/j.laa.2011.06.034en_US
dc.identifier.endpage85
dc.identifier.issn0024-3795en_US
dc.identifier.issn0024-3795
dc.identifier.issue1
dc.identifier.scopus2-s2.0-80055063962en_US
dc.identifier.scopusqualityQ1
dc.identifier.startpage79en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12469/955
dc.identifier.urihttps://doi.org/10.1016/j.laa.2011.06.034
dc.identifier.volume436en_US
dc.identifier.wosWOS:000297431200008en_US
dc.identifier.wosqualityQ2
dc.institutionauthorBilge, Ayşe Hümeyraen_US
dc.language.isoenen_US
dc.publisherElsevier Science Incen_US
dc.relation.journalLinear algebra and its applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAnti-commuting linear operatorsen_US
dc.subjectRepresentations of Clifford algebrasen_US
dc.titleCanonical forms for families of anti-commuting diagonalizable linear operatorsen_US
dc.typeArticleen_US
dspace.entity.typePublication
relation.isAuthorOfPublication1b50a6b2-7290-44da-b8d5-f048fea8b315
relation.isAuthorOfPublication.latestForDiscovery1b50a6b2-7290-44da-b8d5-f048fea8b315

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