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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 |
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Authors | |
Issue Date | 1983 |
Publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa |
Citation | Linear Algebra And Its Applications, 1983, v. 110 C, p. 181-212 How to Cite? |
Abstract | 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. |
Persistent Identifier | http://hdl.handle.net/10722/156225 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.837 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Li, CK | en_US |
dc.contributor.author | Tsing, NK | en_US |
dc.date.accessioned | 2012-08-08T08:40:55Z | - |
dc.date.available | 2012-08-08T08:40:55Z | - |
dc.date.issued | 1983 | en_US |
dc.identifier.citation | Linear Algebra And Its Applications, 1983, v. 110 C, p. 181-212 | en_US |
dc.identifier.issn | 0024-3795 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156225 | - |
dc.description.abstract | 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. | en_US |
dc.language | eng | en_US |
dc.publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa | en_US |
dc.relation.ispartof | Linear Algebra and Its Applications | en_US |
dc.title | Duality between some linear preserver problems. II. Isometries with respect to c-special norms and matrices with fixed singular values | en_US |
dc.type | Article | en_US |
dc.identifier.email | Tsing, NK:nktsing@hku.hk | en_US |
dc.identifier.authority | Tsing, NK=rp00794 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1016/0024-3795(83)90136-2 | - |
dc.identifier.scopus | eid_2-s2.0-48749147527 | en_US |
dc.identifier.volume | 110 | en_US |
dc.identifier.issue | C | en_US |
dc.identifier.spage | 181 | en_US |
dc.identifier.epage | 212 | en_US |
dc.identifier.isi | WOS:A1988Q773400008 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Li, CK=8048590800 | en_US |
dc.identifier.scopusauthorid | Tsing, NK=6602663351 | en_US |
dc.identifier.issnl | 0024-3795 | - |