On the dimension of orbits of matrix pencils under strict equivalence Articles uri icon

publication date

  • January 2026

start page

  • 1

end page

  • 6

issue

  • 109695

volume

  • 172

International Standard Serial Number (ISSN)

  • 0893-9659

Electronic International Standard Serial Number (EISSN)

  • 1873-5452

abstract

  • We prove that, given two matrix pencils L and M, if M belongs to the closure of the orbit of L under strict equivalence, then the dimension of the orbit of M is smaller than or equal to the dimension of the orbit of M, and the equality is only attained when M belongs to the orbit of L. Our proof uses only the majorization involving the eigenstructures of L and M which characterizes the inclusion relationship between orbit closures, together with the formula for the codimension of the orbit of a pencil in terms of its eigenstruture.

subjects

  • Mathematics

keywords

  • matrix pencils; strict equivalence; orbit; closure; codimension; eigenstructure