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Article: On analyticity of functions involving eigenvalues

TitleOn analyticity of functions involving eigenvalues
Authors
Issue Date1994
PublisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa
Citation
Linear Algebra And Its Applications, 1994, v. 207, p. 159-180 How to Cite?
AbstractLet A(z) be an n × n complex matrix whose elements depend analytically on z ∈ Cm. It is well known that any individual eigenvalue of A(z) may be nondifferentiable when it coalesces with others. In this paper, we investigate the analycity property of functions on the eigenvalues λ(z) = (λ1(z),..., λn(z)) of A(z). We first introduce the notion of functions that are symmetric with respect to partitions. It is then shown that if a function f{hook} : Cn → C is analytic at λ(a), where a ε{lunate} Cm, and is symmetric with respect to a certain partition induced by λ(a), then the composite function g(z) = f{hook}(λ1(z),...,λn(z)) is analytic at a. When z is real, A(z) is symmetric or Hermitian, and the aforementioned assumptions hold, so that g(z) is analytic at a, we also derive formulae for its first and second order partial derivatives. We apply the results to several problems involving eigenvalues. © 1994.
Persistent Identifierhttp://hdl.handle.net/10722/75426
ISSN
2015 Impact Factor: 0.965
2015 SCImago Journal Rankings: 0.837
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorTsing, NKen_HK
dc.contributor.authorFan, MKHen_HK
dc.contributor.authorVerriest, EIen_HK
dc.date.accessioned2010-09-06T07:11:00Z-
dc.date.available2010-09-06T07:11:00Z-
dc.date.issued1994en_HK
dc.identifier.citationLinear Algebra And Its Applications, 1994, v. 207, p. 159-180en_HK
dc.identifier.issn0024-3795en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75426-
dc.description.abstractLet A(z) be an n × n complex matrix whose elements depend analytically on z ∈ Cm. It is well known that any individual eigenvalue of A(z) may be nondifferentiable when it coalesces with others. In this paper, we investigate the analycity property of functions on the eigenvalues λ(z) = (λ1(z),..., λn(z)) of A(z). We first introduce the notion of functions that are symmetric with respect to partitions. It is then shown that if a function f{hook} : Cn → C is analytic at λ(a), where a ε{lunate} Cm, and is symmetric with respect to a certain partition induced by λ(a), then the composite function g(z) = f{hook}(λ1(z),...,λn(z)) is analytic at a. When z is real, A(z) is symmetric or Hermitian, and the aforementioned assumptions hold, so that g(z) is analytic at a, we also derive formulae for its first and second order partial derivatives. We apply the results to several problems involving eigenvalues. © 1994.en_HK
dc.languageengen_HK
dc.publisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laaen_HK
dc.relation.ispartofLinear Algebra and Its Applicationsen_HK
dc.rightsLinear Algebra and Its Applications. Copyright © Elsevier Inc.en_HK
dc.titleOn analyticity of functions involving eigenvaluesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0024-3795&volume=207&spage=159&epage=180&date=1994&atitle=On+analyticity+of+functions+involving+eigenvaluesen_HK
dc.identifier.emailTsing, NK:nktsing@hku.hken_HK
dc.identifier.authorityTsing, NK=rp00794en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/0024-3795(94)90009-4-
dc.identifier.scopuseid_2-s2.0-21344492539en_HK
dc.identifier.hkuros6570en_HK
dc.identifier.volume207en_HK
dc.identifier.spage159en_HK
dc.identifier.epage180en_HK
dc.identifier.isiWOS:A1994NY38800009-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridTsing, NK=6602663351en_HK
dc.identifier.scopusauthoridFan, MKH=7201970821en_HK
dc.identifier.scopusauthoridVerriest, EI=35805539700en_HK
dc.customcontrol.immutablecsl 140428-

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