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On the Necessary and Sufficient Condition for a Set of Matrices to Commute and Some Further Linked Results

dc.contributor.authorDe la Sen Parte, Manuel ORCIDes
dc.date.accessioned2011-02-11T17:09:07Zes
dc.date.accessioned2011-03-29T04:51:11Z
dc.date.available2011-02-11T17:09:07Zes
dc.date.available2011-03-29T04:51:11Z
dc.date.issued2009es
dc.identifier.citationMathematical Problems in Engineering 2009 : (2009) // Article ID 650970es
dc.identifier.issn1024-123Xes
dc.identifier.urihttp://hdl.handle.net/10810/2194es
dc.descriptionEs reproducción del documento publicado en http://dx.doi.org/10.1155/2009/650970es
dc.description.abstractThis paper investigates the necessary and sufficient condition for a set of (real or complex) matrices to commute. It is proved that the commutator [A,B]=0 for two matrices A and B if and only if a vector v(B) defined uniquely from the matrix B is in the null space of a well-structured matrix defined as the Kronecker sum A⊕(−A∗), which is always rank defective. This result is extendable directly to any countable set of commuting matrices. Complementary results are derived concerning the commutators of certain matrices with functions of matrices f(A) which extend the well-known sufficiency-type commuting result [A,f(A)]=0.es
dc.description.sponsorshipMinisterio de Educación DPI2006-00714 ; Gobierno Vasco GIC07143-IT-269-07 y SAIOTEK S-PE08UN15es
dc.language.isoenges
dc.publisherHindawi Publishing Corporationes
dc.relationinfo:eu-repo/grantAgreement/MICINN/DPI2006-00714
dc.rightsinfo:eu-repo/semantics/openAccesses
dc.subjectswitched linear-systemses
dc.subjecttime delay systemses
dc.subjectadaptative controles
dc.subjectmultiple modelses
dc.subjectstabilityes
dc.subjecteigenvectorses
dc.subjectmultiestimationes
dc.subjectcommutativityes
dc.subjectschemees
dc.titleOn the Necessary and Sufficient Condition for a Set of Matrices to Commute and Some Further Linked Resultses
dc.typeinfo:eu-repo/semantics/articlees
dc.rights.holderCopyright © 2009 M. De La Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.es
dc.departamentoesElectricidad y electrónicaes_ES
dc.departamentoeuElektrizitatea eta elektronikaes_ES
dc.subject.categoriaENGINEERING
dc.subject.categoriaMATHEMATICS


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