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Article: The numerical range of derivations

TitleThe numerical range of derivations
Authors
Issue Date1989
PublisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa
Citation
Linear Algebra And Its Applications, 1989, v. 119, p. 97-119 How to Cite?
AbstractLet p, q, n be integers satisfying 1 ≤ p ≤ q ≤ n. The (p, q)-numerical range of an n×n complex matrix A is defined by Wp,q(A) = {Ep((UAU*)[q]): U unitary}, where for an n×n complex matrix X, X[q] denotes its q×q leading principal submatrix and Ep(X[q]) denotes the pth elementary symmetric function of the eigenvalues of X[q]. When 1 = p = q, the set reduces to the classical numerical range of A, which is well known to be convex. Many authors have used the concept of classical numerical range to study different classes of matrices. In this note we extend the results to the generalized cases. Besides obtaining new results, we collect existing ones and give alternative proofs for some of them. We also study the (p,q)-numerical radius of A defined by rp,q(A) = max{|μ|:μ ∈ Wp,q(A)}. © 1989.
Persistent Identifierhttp://hdl.handle.net/10722/156146
ISSN
2015 Impact Factor: 0.965
2015 SCImago Journal Rankings: 0.837
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLi, CKen_US
dc.contributor.authorTsing, NKen_US
dc.date.accessioned2012-08-08T08:40:35Z-
dc.date.available2012-08-08T08:40:35Z-
dc.date.issued1989en_US
dc.identifier.citationLinear Algebra And Its Applications, 1989, v. 119, p. 97-119en_US
dc.identifier.issn0024-3795en_US
dc.identifier.urihttp://hdl.handle.net/10722/156146-
dc.description.abstractLet p, q, n be integers satisfying 1 ≤ p ≤ q ≤ n. The (p, q)-numerical range of an n×n complex matrix A is defined by Wp,q(A) = {Ep((UAU*)[q]): U unitary}, where for an n×n complex matrix X, X[q] denotes its q×q leading principal submatrix and Ep(X[q]) denotes the pth elementary symmetric function of the eigenvalues of X[q]. When 1 = p = q, the set reduces to the classical numerical range of A, which is well known to be convex. Many authors have used the concept of classical numerical range to study different classes of matrices. In this note we extend the results to the generalized cases. Besides obtaining new results, we collect existing ones and give alternative proofs for some of them. We also study the (p,q)-numerical radius of A defined by rp,q(A) = max{|μ|:μ ∈ Wp,q(A)}. © 1989.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.titleThe numerical range of derivationsen_US
dc.typeArticleen_US
dc.identifier.emailTsing, NK:nktsing@hku.hken_US
dc.identifier.authorityTsing, NK=rp00794en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/0024-3795(89)90071-2-
dc.identifier.scopuseid_2-s2.0-26444488090en_US
dc.identifier.volume119en_US
dc.identifier.spage97en_US
dc.identifier.epage119en_US
dc.identifier.isiWOS:A1989AH05200007-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLi, CK=8048590800en_US
dc.identifier.scopusauthoridTsing, NK=6602663351en_US
dc.customcontrol.immutablecsl 140428-

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