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Article: Mappings on matrices: Invariance of functional values of matrix products

TitleMappings on matrices: Invariance of functional values of matrix products
Authors
KeywordsUnitary Similarity Invariant Functions
Zero Product Preservers
Issue Date2006
PublisherAustralian Mathematical Society. The Journal's web site is located at http://www.austms.org.au/Publ/JAustMS/
Citation
Journal Of The Australian Mathematical Society, 2006, v. 81 n. 2, p. 165-184 How to Cite?
AbstractLet M n be the algebra of all n × n matrices over a field double-struck F sign, where n ≥ 2. Let S be a subset of M n containing all rank one matrices. We study mappings Φ S → M n such that F(ø) (A)ø(B)) = F(AB) for various families of functions F including all the unitary similarity invariant functions on real or complex matrices. Very often, these mappings have the form A → μ(A) S(σ(a ij))S -1 for all A = (a ij) ∈ S for some invertible S ∈ M n, field monomorphism σ of double-struck F sign*, and an double-struck F sign*-valued mapping μ defined on S. For real matrices, σ is often the identity map; for complex matrices, σ is often the identity map or the conjugation map: z → Ž. A key idea in our study is reducing the problem to the special case when F : M n → {0, 1} is defined by F(X) = 0, if X = 0, and F(X) = 1 otherwise. In such a case, one needs to characterize Φ : S → M n such that Φ (A) Φ (B) = 0 if and only if AB = 0. We show that such a map has the standard form described above on rank one matrices in S. © 2006 Australian Mathematical Society.
Persistent Identifierhttp://hdl.handle.net/10722/156175
ISSN
2015 Impact Factor: 0.443
2015 SCImago Journal Rankings: 0.255
References

 

DC FieldValueLanguage
dc.contributor.authorChan, JTen_US
dc.contributor.authorLi, CKen_US
dc.contributor.authorSze, NSen_US
dc.date.accessioned2012-08-08T08:40:43Z-
dc.date.available2012-08-08T08:40:43Z-
dc.date.issued2006en_US
dc.identifier.citationJournal Of The Australian Mathematical Society, 2006, v. 81 n. 2, p. 165-184en_US
dc.identifier.issn1446-7887en_US
dc.identifier.urihttp://hdl.handle.net/10722/156175-
dc.description.abstractLet M n be the algebra of all n × n matrices over a field double-struck F sign, where n ≥ 2. Let S be a subset of M n containing all rank one matrices. We study mappings Φ S → M n such that F(ø) (A)ø(B)) = F(AB) for various families of functions F including all the unitary similarity invariant functions on real or complex matrices. Very often, these mappings have the form A → μ(A) S(σ(a ij))S -1 for all A = (a ij) ∈ S for some invertible S ∈ M n, field monomorphism σ of double-struck F sign*, and an double-struck F sign*-valued mapping μ defined on S. For real matrices, σ is often the identity map; for complex matrices, σ is often the identity map or the conjugation map: z → Ž. A key idea in our study is reducing the problem to the special case when F : M n → {0, 1} is defined by F(X) = 0, if X = 0, and F(X) = 1 otherwise. In such a case, one needs to characterize Φ : S → M n such that Φ (A) Φ (B) = 0 if and only if AB = 0. We show that such a map has the standard form described above on rank one matrices in S. © 2006 Australian Mathematical Society.en_US
dc.languageengen_US
dc.publisherAustralian Mathematical Society. The Journal's web site is located at http://www.austms.org.au/Publ/JAustMS/en_US
dc.relation.ispartofJournal of the Australian Mathematical Societyen_US
dc.rightsJournal of the Australian Mathematical Society. Copyright © Australian Mathematical Society.-
dc.subjectUnitary Similarity Invariant Functionsen_US
dc.subjectZero Product Preserversen_US
dc.titleMappings on matrices: Invariance of functional values of matrix productsen_US
dc.typeArticleen_US
dc.identifier.emailChan, JT:jtchan@hkucc.hku.hken_US
dc.identifier.authorityChan, JT=rp00663en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1017/S1446788700015809en_US
dc.identifier.scopuseid_2-s2.0-33845245426en_US
dc.identifier.hkuros127729-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33845245426&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume81en_US
dc.identifier.issue2en_US
dc.identifier.spage165en_US
dc.identifier.epage184en_US
dc.identifier.eissn1446-8107-
dc.publisher.placeAustraliaen_US
dc.identifier.scopusauthoridChan, JT=8246867400en_US
dc.identifier.scopusauthoridLi, CK=8048590800en_US
dc.identifier.scopusauthoridSze, NS=7003280174en_US

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