Generic symmetric matrix pencils with bounded rank Articles uri icon

publication date

  • September 2020

start page

  • 905

end page

  • 926

issue

  • 3

volume

  • 10

International Standard Serial Number (ISSN)

  • 1664-039X

abstract

  • We show that the set of n × n complex symmetric matrix pencils of rank at mostr is the union of the closures of [r/2] + 1 sets of matrix pencils with some, explicitly described,complete eigenstructures. As a consequence, these are the generic complete eigenstructures of n × ncomplex symmetric matrix pencils of rank at most r. We also show that these closures correspondto the irreducible components of the set of n ×n symmetric matrix pencils with rank at most r whenconsidered as an algebraic set.

keywords

  • matrix pencil; symmetric pencil; strict equivalence; congruence; orbit; bundle; spectral information; complete eigenstructure