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Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree
Department of Computing Science, Umeå University, Umeå, Sweden.ORCID iD: 0000-0001-9110-6182
Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain.
2017 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 535, p. 213-230Article in journal (Refereed) Published
Abstract [en]

The set POLd,rm×n of m×n complex matrix polynomials of grade d and (normal) rank at most r in a complex (d+1)mn dimensional space is studied. For r=1,...,min{m,n}−1, we show that POLd,rm×n is the union of the closures of the rd+1 sets of matrix polynomials with rank r, degree exactly d, and explicitly described complete eigenstructures. In addition, for the full-rank rectangular polynomials, i.e. r=min{m,n} and mn, we show that POLd,rm×n coincides with the closure of a single set of the polynomials with rank r, degree exactly d, and the described complete eigenstructure. These complete eigenstructures correspond to generic m×n matrix polynomials of grade d and rank at most r.

Place, publisher, year, edition, pages
Elsevier , 2017. Vol. 535, p. 213-230
Keywords [en]
Complete eigenstructure, Genericity, Matrix polynomials, Normal rank, Orbits
National Category
Computer Sciences Algebra and Logic
Identifiers
URN: urn:nbn:se:oru:diva-74881DOI: 10.1016/j.laa.2017.09.007ISI: 000413058000012Scopus ID: 2-s2.0-85029308799OAI: oai:DiVA.org:oru-74881DiVA, id: diva2:1332908
Funder
Swedish Research Council, E0485301eSSENCE - An eScience CollaborationStiftelsen Längmanska kulturfonden, BA17-1175Available 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
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  • 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
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