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Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Universidad Carlos III de Madrid.
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 and Information Sciences Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-139923DOI: 10.1016/j.laa.2017.09.007ISI: 000413058000012OAI: oai:DiVA.org:umu-139923DiVA, id: diva2:1144635
Funder
Swedish Research Council, E0485301Swedish Research Council, eSSENCEStiftelsen Längmanska kulturfonden, BA17-1175Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-06-09Bibliographically approved

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Dmytryshyn, Andrii

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