Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree Articles uri icon

publication date

  • December 2017

start page

  • 213

end page

  • 230

volume

  • 535

International Standard Serial Number (ISSN)

  • 0024-3795

Electronic International Standard Serial Number (EISSN)

  • 1873-1856

abstract

  • The set POLd,rmxn of m x 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,rmxn 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 = n} and m not equal n, we show that POLd,rmxn 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 x n matrix polynomials of grade d and rank at most r. (C) 2017 Elsevier Inc. All rights reserved.

keywords

  • complete eigenstructure; genericity; matrix polynomials; normal rank; orbits