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Article: The constrained bilinear form and the C-numerical range
Title | The constrained bilinear form and the C-numerical range |
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Authors | |
Issue Date | 1984 |
Publisher | Elsevier 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? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/156092 |
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 | Tsing, NK | en_US |
dc.date.accessioned | 2012-08-08T08:40:22Z | - |
dc.date.available | 2012-08-08T08:40:22Z | - |
dc.date.issued | 1984 | en_US |
dc.identifier.citation | Linear Algebra And Its Applications, 1984, v. 56 C, p. 195-206 | en_US |
dc.identifier.issn | 0024-3795 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156092 | - |
dc.description.abstract | Let 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.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 | The constrained bilinear form and the C-numerical range | 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(84)90125-3 | - |
dc.identifier.scopus | eid_2-s2.0-0037749343 | en_US |
dc.identifier.volume | 56 | en_US |
dc.identifier.issue | C | en_US |
dc.identifier.spage | 195 | en_US |
dc.identifier.epage | 206 | en_US |
dc.identifier.isi | WOS:A1984RW58700017 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Tsing, NK=6602663351 | en_US |
dc.identifier.issnl | 0024-3795 | - |