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Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Universidad Carlos III de Madrid.
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
Computing Science
Identifiers
URN: urn:nbn:se:umu:diva-139925DOI: 10.1016/j.laa.2017.09.006ISI: 000414814500001OAI: oai:DiVA.org:umu-139925DiVA, id: diva2:1144638
Funder
Swedish Research Council, E0485301Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-06-09Bibliographically approved

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Dmytryshyn, Andrii

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