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Article: Inertia and rank characterizations of some matrix expressions

TitleInertia and rank characterizations of some matrix expressions
Authors
KeywordsCompletion
Inertia
Matrix equation
Partial matrix
Rank
Issue Date2009
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX
Citation
SIAM Journal On Matrix Analysis And Applications, 2009, v. 31 n. 3, p. 1187-1226 How to Cite?
Abstract
In this paper we consider the admissible inertias and ranks of the expressions A - BXB* - CY C* and A - BXC* ± CX*B* with unknowns X and Y in the four cases when these expressions are: (i) complex self-adjoint, (ii) complex skew-adjoint, (iii) real symmetric, (iv) real skew symmetric. We also provide a construction for X and Y to achieve the desired inertia/rank that uses only unitary/orthogonal transformation, thus leading to a numerically reliable construction. In addition, we look at related block matrix completion problems [A ±B* ±C * B X ±E* C E Y] with either two diagonal unknown blocks and [A ±B* ±X * B D ±C* X C E] with an unknown off-diagonal block. Finally, we also provide all admissible ranks in the case when we drop any adjointness/symmetry constraint. © 2009 Society for Industrial and Applied Mathematics.
Persistent Identifierhttp://hdl.handle.net/10722/124722
ISSN
2013 Impact Factor: 1.806
ISI Accession Number ID
Funding AgencyGrant Number
NSFDMS-0500678
Funding Information:

This author's research was partially supported by NSF grant DMS-0500678.

References

 

Author Affiliations
  1. The University of Hong Kong
  2. National University of Singapore
  3. Drexel University
DC FieldValueLanguage
dc.contributor.authorChu, Den_HK
dc.contributor.authorHung, YSen_HK
dc.contributor.authorWoerdeman, HJen_HK
dc.date.accessioned2010-10-31T10:50:25Z-
dc.date.available2010-10-31T10:50:25Z-
dc.date.issued2009en_HK
dc.identifier.citationSIAM Journal On Matrix Analysis And Applications, 2009, v. 31 n. 3, p. 1187-1226en_HK
dc.identifier.issn0895-4798en_HK
dc.identifier.urihttp://hdl.handle.net/10722/124722-
dc.description.abstractIn this paper we consider the admissible inertias and ranks of the expressions A - BXB* - CY C* and A - BXC* ± CX*B* with unknowns X and Y in the four cases when these expressions are: (i) complex self-adjoint, (ii) complex skew-adjoint, (iii) real symmetric, (iv) real skew symmetric. We also provide a construction for X and Y to achieve the desired inertia/rank that uses only unitary/orthogonal transformation, thus leading to a numerically reliable construction. In addition, we look at related block matrix completion problems [A ±B* ±C * B X ±E* C E Y] with either two diagonal unknown blocks and [A ±B* ±X * B D ±C* X C E] with an unknown off-diagonal block. Finally, we also provide all admissible ranks in the case when we drop any adjointness/symmetry constraint. © 2009 Society for Industrial and Applied Mathematics.en_HK
dc.languageengen_HK
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SIMAXen_HK
dc.relation.ispartofSIAM Journal on Matrix Analysis and Applicationsen_HK
dc.rightsS I A M Journal on Matrix Analysis and Applications. Copyright © Society for Industrial and Applied Mathematics.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectCompletionen_HK
dc.subjectInertiaen_HK
dc.subjectMatrix equationen_HK
dc.subjectPartial matrixen_HK
dc.subjectRanken_HK
dc.titleInertia and rank characterizations of some matrix expressionsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0895-4798&volume=31&issue=3&spage=1187&epage=1226&date=2009&atitle=Inertia+and+rank+characterizations+of+some+matrix+expressions-
dc.identifier.emailHung, YS:yshung@eee.hku.hken_HK
dc.identifier.authorityHung, YS=rp00220en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1137/080712945en_HK
dc.identifier.scopuseid_2-s2.0-72449170482en_HK
dc.identifier.hkuros175052en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-72449170482&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume31en_HK
dc.identifier.issue3en_HK
dc.identifier.spage1187en_HK
dc.identifier.epage1226en_HK
dc.identifier.isiWOS:000271800100019-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChu, D=7201734138en_HK
dc.identifier.scopusauthoridHung, YS=8091656200en_HK
dc.identifier.scopusauthoridWoerdeman, HJ=6701873999en_HK

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