English

On characteristic invariants of matrix pencils and linear relations

Spectral Theory 2022-03-17 v1

Abstract

The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic and the Kronecker canonical form of the pencil. This relationship is exploited to obtain estimations on the invariant characteristics of matrix pencils under rank one perturbations.

Keywords

Cite

@article{arxiv.2203.08296,
  title  = {On characteristic invariants of matrix pencils and linear relations},
  author = {Hannes Gernandt and Francisco Martínez Pería and Friedrich Philipp and Carsten Trunk},
  journal= {arXiv preprint arXiv:2203.08296},
  year   = {2022}
}