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Article: Inertia and rank characterizations of some matrix expressions
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TitleInertia and rank characterizations of some matrix expressions
 
AuthorsChu, D2
Hung, YS1
Woerdeman, HJ3
 
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
 
CitationSIAM Journal On Matrix Analysis And Applications, 2009, v. 31 n. 3, p. 1187-1226 [How to Cite?]
DOI: http://dx.doi.org/10.1137/080712945
 
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.
 
ISSN0895-4798
2012 Impact Factor: 1.342
2012 SCImago Journal Rankings: 1.509
 
DOIhttp://dx.doi.org/10.1137/080712945
 
ISI Accession Number IDWOS:000271800100019
Funding AgencyGrant Number
NSFDMS-0500678
Funding Information:

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

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorChu, D
 
dc.contributor.authorHung, YS
 
dc.contributor.authorWoerdeman, HJ
 
dc.date.accessioned2010-10-31T10:50:25Z
 
dc.date.available2010-10-31T10:50:25Z
 
dc.date.issued2009
 
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.
 
dc.description.naturepublished_or_final_version
 
dc.identifier.citationSIAM Journal On Matrix Analysis And Applications, 2009, v. 31 n. 3, p. 1187-1226 [How to Cite?]
DOI: http://dx.doi.org/10.1137/080712945
 
dc.identifier.doihttp://dx.doi.org/10.1137/080712945
 
dc.identifier.epage1226
 
dc.identifier.hkuros175052
 
dc.identifier.isiWOS:000271800100019
Funding AgencyGrant Number
NSFDMS-0500678
Funding Information:

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

 
dc.identifier.issn0895-4798
2012 Impact Factor: 1.342
2012 SCImago Journal Rankings: 1.509
 
dc.identifier.issue3
 
dc.identifier.openurl
 
dc.identifier.scopuseid_2-s2.0-72449170482
 
dc.identifier.spage1187
 
dc.identifier.urihttp://hdl.handle.net/10722/124722
 
dc.identifier.volume31
 
dc.languageeng
 
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX
 
dc.publisher.placeUnited States
 
dc.relation.ispartofSIAM Journal on Matrix Analysis and Applications
 
dc.relation.referencesReferences in Scopus
 
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.subjectCompletion
 
dc.subjectInertia
 
dc.subjectMatrix equation
 
dc.subjectPartial matrix
 
dc.subjectRank
 
dc.titleInertia and rank characterizations of some matrix expressions
 
dc.typeArticle
 
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<subject>Completion</subject>
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Author Affiliations
  1. The University of Hong Kong
  2. National University of Singapore
  3. Drexel University