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Article: Mappings preserving spectra of products of matrices

TitleMappings preserving spectra of products of matrices
Authors
Keywordseigenvalue
spectrum
preserve
Issue Date2007
PublisherAmerican Mathematical Society. The Journal's web site is located at http://www.ams.org/proc
Citation
Proceedings Of The American Mathematical Society, 2007, v. 135 n. 4, p. 977-986 How to Cite?
AbstractLet Mn be the set of n × n complex matrices, and for every A ε Mn, let Sp(A) denote the spectrum of A. For various types of products A1* • • • * Aκk on Mn, it is shown that a mapping η:Mn → M n satisfying Sp(A1* • • • * Aκ) = Sp(ηp(A1) * • • • * η(Aκ)) for all A1,.,Aκ ε Mn has the form X →ψ.S-1XS or A →η S-1X tS for some invertible S ε Mn and scalar ε. The result covers the special cases of the usual product A1 * • • • * Aκ = A1 • • •Aκ, the Jordan triple product A1 *A 2 = A1 *A2 *A1, and the Jordan product A1 *A2 = (A1A2 +A2A1/2. Similar results are obtained for Hermitian matrices. © 2006 American Mathematical Society.
Persistent Identifierhttp://hdl.handle.net/10722/44899
ISSN
2015 Impact Factor: 0.7
2015 SCImago Journal Rankings: 1.082
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChan, JTen_HK
dc.contributor.authorLi, CKen_HK
dc.contributor.authorSze, NSen_HK
dc.date.accessioned2007-10-30T06:12:57Z-
dc.date.available2007-10-30T06:12:57Z-
dc.date.issued2007en_HK
dc.identifier.citationProceedings Of The American Mathematical Society, 2007, v. 135 n. 4, p. 977-986en_HK
dc.identifier.issn0002-9939en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44899-
dc.description.abstractLet Mn be the set of n × n complex matrices, and for every A ε Mn, let Sp(A) denote the spectrum of A. For various types of products A1* • • • * Aκk on Mn, it is shown that a mapping η:Mn → M n satisfying Sp(A1* • • • * Aκ) = Sp(ηp(A1) * • • • * η(Aκ)) for all A1,.,Aκ ε Mn has the form X →ψ.S-1XS or A →η S-1X tS for some invertible S ε Mn and scalar ε. The result covers the special cases of the usual product A1 * • • • * Aκ = A1 • • •Aκ, the Jordan triple product A1 *A 2 = A1 *A2 *A1, and the Jordan product A1 *A2 = (A1A2 +A2A1/2. Similar results are obtained for Hermitian matrices. © 2006 American Mathematical Society.en_HK
dc.format.extent179879 bytes-
dc.format.extent664 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherAmerican Mathematical Society. The Journal's web site is located at http://www.ams.org/procen_HK
dc.relation.ispartofProceedings of the American Mathematical Societyen_HK
dc.rightsFirst published in American Mathematical Society Proceedings, 2006, v. 135 n. 4, p. 977-986 published by the American Mathematical Society,en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjecteigenvalueen_HK
dc.subjectspectrumen_HK
dc.subjectpreserveen_HK
dc.titleMappings preserving spectra of products of matricesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0002-9939&volume=135&issue=4&spage=977&epage=986&date=2006&atitle=Mappings+preserving+spectra+of+products+of+matricesen_HK
dc.identifier.emailChan, JT:jtchan@hkucc.hku.hken_HK
dc.identifier.authorityChan, JT=rp00663en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1090/S0002-9939-06-08568-6en_HK
dc.identifier.scopuseid_2-s2.0-35549005382en_HK
dc.identifier.hkuros127730-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-35549005382&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume135en_HK
dc.identifier.issue4en_HK
dc.identifier.spage977en_HK
dc.identifier.epage986en_HK
dc.identifier.eissn1088-6826-
dc.identifier.isiWOS:000242238500006-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChan, JT=8246867400en_HK
dc.identifier.scopusauthoridLi, CK=8048590800en_HK
dc.identifier.scopusauthoridSze, NS=7003280174en_HK

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