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

Authors  
Keywords  Unitary Similarity Invariant Functions Zero Product Preservers 
Issue Date  2006 
Publisher  Australian 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. 165184 How to Cite? 
Abstract  Let M n be the algebra of all n × n matrices over a field doublestruck 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 doublestruck F sign*, and an doublestruck 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 Identifier  http://hdl.handle.net/10722/156175 
ISSN  2015 Impact Factor: 0.443 2015 SCImago Journal Rankings: 0.255 
References 
DC Field  Value  Language 

dc.contributor.author  Chan, JT  en_US 
dc.contributor.author  Li, CK  en_US 
dc.contributor.author  Sze, NS  en_US 
dc.date.accessioned  20120808T08:40:43Z   
dc.date.available  20120808T08:40:43Z   
dc.date.issued  2006  en_US 
dc.identifier.citation  Journal Of The Australian Mathematical Society, 2006, v. 81 n. 2, p. 165184  en_US 
dc.identifier.issn  14467887  en_US 
dc.identifier.uri  http://hdl.handle.net/10722/156175   
dc.description.abstract  Let M n be the algebra of all n × n matrices over a field doublestruck 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 doublestruck F sign*, and an doublestruck 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.language  eng  en_US 
dc.publisher  Australian Mathematical Society. The Journal's web site is located at http://www.austms.org.au/Publ/JAustMS/  en_US 
dc.relation.ispartof  Journal of the Australian Mathematical Society  en_US 
dc.rights  Journal of the Australian Mathematical Society. Copyright © Australian Mathematical Society.   
dc.subject  Unitary Similarity Invariant Functions  en_US 
dc.subject  Zero Product Preservers  en_US 
dc.title  Mappings on matrices: Invariance of functional values of matrix products  en_US 
dc.type  Article  en_US 
dc.identifier.email  Chan, JT:jtchan@hkucc.hku.hk  en_US 
dc.identifier.authority  Chan, JT=rp00663  en_US 
dc.description.nature  link_to_subscribed_fulltext  en_US 
dc.identifier.doi  10.1017/S1446788700015809  en_US 
dc.identifier.scopus  eid_2s2.033845245426  en_US 
dc.identifier.hkuros  127729   
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.033845245426&selection=ref&src=s&origin=recordpage  en_US 
dc.identifier.volume  81  en_US 
dc.identifier.issue  2  en_US 
dc.identifier.spage  165  en_US 
dc.identifier.epage  184  en_US 
dc.identifier.eissn  14468107   
dc.publisher.place  Australia  en_US 
dc.identifier.scopusauthorid  Chan, JT=8246867400  en_US 
dc.identifier.scopusauthorid  Li, CK=8048590800  en_US 
dc.identifier.scopusauthorid  Sze, NS=7003280174  en_US 