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Article: On analyticity of functions involving eigenvalues
Title | On analyticity of functions involving eigenvalues |
---|---|
Authors | |
Issue Date | 1994 |
Publisher | Elsevier 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? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/75426 |
ISSN | 2015 Impact Factor: 0.965 2015 SCImago Journal Rankings: 0.837 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Tsing, NK | en_HK |
dc.contributor.author | Fan, MKH | en_HK |
dc.contributor.author | Verriest, EI | en_HK |
dc.date.accessioned | 2010-09-06T07:11:00Z | - |
dc.date.available | 2010-09-06T07:11:00Z | - |
dc.date.issued | 1994 | en_HK |
dc.identifier.citation | Linear Algebra And Its Applications, 1994, v. 207, p. 159-180 | en_HK |
dc.identifier.issn | 0024-3795 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75426 | - |
dc.description.abstract | Let 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.language | eng | en_HK |
dc.publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa | en_HK |
dc.relation.ispartof | Linear Algebra and Its Applications | en_HK |
dc.rights | Linear Algebra and Its Applications. Copyright © Elsevier Inc. | en_HK |
dc.title | On analyticity of functions involving eigenvalues | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+eigenvalues | en_HK |
dc.identifier.email | Tsing, NK:nktsing@hku.hk | en_HK |
dc.identifier.authority | Tsing, NK=rp00794 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/0024-3795(94)90009-4 | - |
dc.identifier.scopus | eid_2-s2.0-21344492539 | en_HK |
dc.identifier.hkuros | 6570 | en_HK |
dc.identifier.volume | 207 | en_HK |
dc.identifier.spage | 159 | en_HK |
dc.identifier.epage | 180 | en_HK |
dc.identifier.isi | WOS:A1994NY38800009 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Tsing, NK=6602663351 | en_HK |
dc.identifier.scopusauthorid | Fan, MKH=7201970821 | en_HK |
dc.identifier.scopusauthorid | Verriest, EI=35805539700 | en_HK |
dc.customcontrol.immutable | csl 140428 | - |