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Article: Duality between some linear preserver problems. II. Isometries with respect to c-special norms and matrices with fixed singular values

Title Duality between some linear preserver problems. II. Isometries with respect to c-special norms and matrices with fixed singular values Li, CKTsing, NK 1983 Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa Linear Algebra And Its Applications, 1983, v. 110 C, p. 181-212 How to Cite? Let Fm×n (m≤n) denote the linear space of all m × n complex or real matrices according as F=C or R. Let c=(c1,...,cm)≠0 be such that c1≥⋯≥cm≥0. The c-spectral norm of a matrix Aε{lunate}Fm×n is the quantity {norm of matrix}A{norm of matrix}c ∑ i=I mciσi(A). where σ1(A)≥⋯≥σm(A) are the singular values of A. Let d=(d1,...,dm)≠0, where d1≥⋯≥dm≥0. We consider the linear isometries between the normed spaces (Fm×n,∥·∥c) and (Fm×n,∥·∥d), and prove that they are dual transformations of the linear operators which map L(d) onto L(c), where L(c)= {Xε{lunate}Fm×n:X has singular values c1,...,cm}. © 1988. http://hdl.handle.net/10722/156225 0024-37952019 Impact Factor: 0.9882015 SCImago Journal Rankings: 0.837

DC FieldValueLanguage
dc.contributor.authorLi, CKen_US
dc.contributor.authorTsing, NKen_US
dc.date.accessioned2012-08-08T08:40:55Z-
dc.date.available2012-08-08T08:40:55Z-
dc.date.issued1983en_US
dc.identifier.citationLinear Algebra And Its Applications, 1983, v. 110 C, p. 181-212en_US
dc.identifier.issn0024-3795en_US
dc.identifier.urihttp://hdl.handle.net/10722/156225-
dc.description.abstractLet Fm×n (m≤n) denote the linear space of all m × n complex or real matrices according as F=C or R. Let c=(c1,...,cm)≠0 be such that c1≥⋯≥cm≥0. The c-spectral norm of a matrix Aε{lunate}Fm×n is the quantity {norm of matrix}A{norm of matrix}c ∑ i=I mciσi(A). where σ1(A)≥⋯≥σm(A) are the singular values of A. Let d=(d1,...,dm)≠0, where d1≥⋯≥dm≥0. We consider the linear isometries between the normed spaces (Fm×n,∥·∥c) and (Fm×n,∥·∥d), and prove that they are dual transformations of the linear operators which map L(d) onto L(c), where L(c)= {Xε{lunate}Fm×n:X has singular values c1,...,cm}. © 1988.en_US
dc.languageengen_US
dc.publisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laaen_US
dc.relation.ispartofLinear Algebra and Its Applicationsen_US
dc.titleDuality between some linear preserver problems. II. Isometries with respect to c-special norms and matrices with fixed singular valuesen_US
dc.typeArticleen_US
dc.identifier.emailTsing, NK:nktsing@hku.hken_US
dc.identifier.authorityTsing, NK=rp00794en_US
dc.identifier.doi10.1016/0024-3795(83)90136-2-
dc.identifier.scopuseid_2-s2.0-48749147527en_US
dc.identifier.volume110en_US
dc.identifier.issueCen_US
dc.identifier.spage181en_US
dc.identifier.epage212en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLi, CK=8048590800en_US
dc.identifier.scopusauthoridTsing, NK=6602663351en_US