Even grade generic skew-symmetric matrix polynomials with bounded rank Articles uri icon

publication date

  • December 2024

start page

  • 218

end page

  • 239

volume

  • 702

International Standard Serial Number (ISSN)

  • 0024-3795

Electronic International Standard Serial Number (EISSN)

  • 1873-1856

abstract

  • We show that the set of 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 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].

subjects

  • Mathematics

keywords

  • complete eigenstructure; genericity; matrix polynomials; skew-symmetry; normal rank; orbits; pencils