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Article: The constrained bilinear form and the C-numerical range

TitleThe constrained bilinear form and the C-numerical range
Authors
Issue Date1984
PublisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa
Citation
Linear Algebra And Its Applications, 1984, v. 56 C, p. 195-206 How to Cite?
AbstractLet V be an n-dimentional unitary space with inner product (·,·) and S the set {x∈V:(x, x)=1}. For any A∈Hom(V, V) and q∈C with {divides}q{divides}≤1, we define W(A:q)={(Ax, y):x, y∈S, (x, y)=q}. If q=1, then W(A:q) is just the classical numerical range {(Ax, x):x∈S}, the convexity of which is well known. Another generalization of the numerical range is the C-numerical range, which is defined to be the set WC(A)={tr(CU*AU):U unitary} where C∈Hom(V, V). In this note, we prove that W(A:q) is always convex and that WC(A) is convex for all A if rank C=1 or n=2. © 1984.
Persistent Identifierhttp://hdl.handle.net/10722/156092
ISSN
2015 Impact Factor: 0.965
2015 SCImago Journal Rankings: 0.837
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorTsing, NKen_US
dc.date.accessioned2012-08-08T08:40:22Z-
dc.date.available2012-08-08T08:40:22Z-
dc.date.issued1984en_US
dc.identifier.citationLinear Algebra And Its Applications, 1984, v. 56 C, p. 195-206en_US
dc.identifier.issn0024-3795en_US
dc.identifier.urihttp://hdl.handle.net/10722/156092-
dc.description.abstractLet V be an n-dimentional unitary space with inner product (·,·) and S the set {x∈V:(x, x)=1}. For any A∈Hom(V, V) and q∈C with {divides}q{divides}≤1, we define W(A:q)={(Ax, y):x, y∈S, (x, y)=q}. If q=1, then W(A:q) is just the classical numerical range {(Ax, x):x∈S}, the convexity of which is well known. Another generalization of the numerical range is the C-numerical range, which is defined to be the set WC(A)={tr(CU*AU):U unitary} where C∈Hom(V, V). In this note, we prove that W(A:q) is always convex and that WC(A) is convex for all A if rank C=1 or n=2. © 1984.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 constrained bilinear form and the C-numerical rangeen_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(84)90125-3-
dc.identifier.scopuseid_2-s2.0-0037749343en_US
dc.identifier.volume56en_US
dc.identifier.issueCen_US
dc.identifier.spage195en_US
dc.identifier.epage206en_US
dc.identifier.isiWOS:A1984RW58700017-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridTsing, NK=6602663351en_US

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