Publication:
Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade

Thumbnail Image
Identifiers
URI: https://hdl.handle.net/10016/32253
ISSN: 0024-3795
DOI: https://doi.org/10.1016/j.laa.2017.09.006
UXXI: AR/0000020651
Files
Generic_LAIA_2018_ps.pdf (584.98 KB)
Publication date
2018-01-01
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
We show that the set of m x 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 x 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).
Description
Keywords
Complete eigenstructure, Genericity, Matrix polynomials, Skew-symmetry, Normal rank, Orbits, Pencils
Bibliographic citation
Dmytryshyn, A. & Dopico, F. M. (2018). Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade. Linear Algebra and Its Applications, 536, pp. 1–18.
Collections
DM - AMCSS - Artículos de Revistas