Even grade generic skew-symmetric matrix polynomials with bounded rank
2024 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 702, p. 218-239Article in journal (Refereed) Published
Abstract [en]
We show that the set of m x m complex skew-symmetric matrix polynomials of even 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 certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic m x m complex skew-symmetric matrix polynomials of even grade d and rank at most 2r. The analogous problem for the case of skew-symmetric matrix polynomials of odd grade is solved in [24].
Place, publisher, year, edition, pages
Elsevier, 2024. Vol. 702, p. 218-239
Keywords [en]
Complete eigenstructure, Genericity, Matrix polynomials, Skew-symmetry, Normal rank, Orbits, Pencils
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-116495DOI: 10.1016/j.laa.2024.07.024ISI: 001316951000001Scopus ID: 2-s2.0-85202293137OAI: oai:DiVA.org:oru-116495DiVA, id: diva2:1904439
Funder
Swedish Research Council, 2021-05393
Note
The work of A. Dmytryshyn was supported by the Swedish Research Council (VR) grant 2021-05393. The work of F. De Teran and F.M. Dopico has been partially funded by the Agencia Estatal de Investigacion of Spain through grants PID2019-106362GB-I00 MCIN/AEI/10.13039/501100011033/and RED2022-134176-T, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23) , and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).
2024-10-092024-10-092024-10-09Bibliographically approved