Article: Inertia and rank characterizations of some matrix expressions
File Download
Links for fulltext
(May Require Subscription)
(May Require Subscription)
- Publisher Website: 10.1137/080712945
- Scopus: eid_2-s2.0-72449170482
- Find via
Supplementary
-
Citations:
-
Appears in Collections:
| Title | Inertia and rank characterizations of some matrix expressions | ||||
|---|---|---|---|---|---|
| Authors | Chu, D2 Hung, YS1 Woerdeman, HJ3 | ||||
| Keywords | Completion Inertia Matrix equation Partial matrix Rank | ||||
| Issue Date | 2009 | ||||
| Publisher | Society 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?] DOI: http://dx.doi.org/10.1137/080712945 | ||||
| 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. | ||||
| ISSN | 0895-4798 2011 Impact Factor: 1.368 2011 SCImago Journal Rankings: 0.069 | ||||
| DOI | http://dx.doi.org/10.1137/080712945 | ||||
| ISI Accession Number ID | WOS:000271800100019
Funding Information: This author's research was partially supported by NSF grant DMS-0500678. | ||||
| References | References in Scopus |
| dc.contributor.author | Chu, D | ||||
|---|---|---|---|---|---|
| dc.contributor.author | Hung, YS | ||||
| dc.contributor.author | Woerdeman, HJ | ||||
| dc.date.accessioned | 2010-10-31T10:50:25Z | ||||
| dc.date.available | 2010-10-31T10:50:25Z | ||||
| dc.date.issued | 2009 | ||||
| dc.description.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. | ||||
| dc.description.nature | published_or_final_version | ||||
| dc.identifier.citation | Siam 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.doi | http://dx.doi.org/10.1137/080712945 | ||||
| dc.identifier.epage | 1226 | ||||
| dc.identifier.hkuros | 175052 | ||||
| dc.identifier.isi | WOS:000271800100019
Funding Information: This author's research was partially supported by NSF grant DMS-0500678. | ||||
| dc.identifier.issn | 0895-4798 2011 Impact Factor: 1.368 2011 SCImago Journal Rankings: 0.069 | ||||
| dc.identifier.issue | 3 | ||||
| dc.identifier.openurl | | ||||
| dc.identifier.scopus | eid_2-s2.0-72449170482 | ||||
| dc.identifier.spage | 1187 | ||||
| dc.identifier.uri | http://hdl.handle.net/10722/124722 | ||||
| dc.identifier.volume | 31 | ||||
| dc.language | eng | ||||
| dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX | ||||
| dc.publisher.place | United States | ||||
| dc.relation.ispartof | SIAM Journal on Matrix Analysis and Applications | ||||
| dc.relation.references | References in Scopus | ||||
| dc.rights | S I A M Journal on Matrix Analysis and Applications. Copyright © Society for Industrial and Applied Mathematics. | ||||
| dc.rights | Creative Commons: Attribution 3.0 Hong Kong License | ||||
| dc.subject | Completion | ||||
| dc.subject | Inertia | ||||
| dc.subject | Matrix equation | ||||
| dc.subject | Partial matrix | ||||
| dc.subject | Rank | ||||
| dc.title | Inertia and rank characterizations of some matrix expressions | ||||
| dc.type | Article |
Author Affiliations
- The University of Hong Kong
- National University of Singapore
- Drexel University