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Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade
Department of Computing Science, Umeå University, Umeå, Sweden.ORCID iD: 0000-0001-9110-6182
Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain.
2018 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 536, p. 1-18Article in journal (Refereed) Published
Abstract [en]

We show that the set of m×m complex skew-symmetric matrix polynomials of odd grade d, i.e., of degree at most d, and (normal) rank at most 2r is the closure of the single set of matrix polynomials with the certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic m×m complex skew-symmetric matrix polynomials of odd grade d and rank at most 2r. In particular, this result includes the case of skew-symmetric matrix pencils (d=1).

Place, publisher, year, edition, pages
Elsevier , 2018. Vol. 536, p. 1-18
Keywords [en]
Complete eigenstructure, Genericity, Matrix polynomials, Skew-symmetry, Normal rank, Orbits, Pencils
National Category
Algebra and Logic
Research subject
business data processing
Identifiers
URN: urn:nbn:se:oru:diva-74880DOI: 10.1016/j.laa.2017.09.006ISI: 000414814500001Scopus ID: 2-s2.0-85029546242OAI: oai:DiVA.org:oru-74880DiVA, id: diva2:1332906
Funder
Swedish Research Council, E0485301eSSENCE - An eScience Collaboration
Note

Research funders:

Ministerio de Economía, Industria y Competitividad of Spain

Fondo Europeo de Desarrollo Regional (FEDER) of EU

Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved

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Dmytryshyn, Andrii

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf