Rank-one perturbations of matrix pencils

TL;DR

This paper characterizes how the Kronecker structure of a matrix pencil changes when subjected to a rank-one perturbation, providing a comprehensive understanding applicable over any field.

Contribution

It offers a complete characterization of the Kronecker structure of matrix pencils after rank-one perturbations, extending previous results to arbitrary fields.

Findings

Explicit description of Kronecker structure changes

Results valid over any field

Provides tools for analyzing perturbations in matrix pencils

Abstract

We solve the problem of characterizing the Kronecker structure of a matrix pencil obtained by a rank-one perturbation of another matrix pencil. The results hold over arbitrary fields.