Fixed rank perturbations of regular 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.

Direct and Inverse Spectral Problems for Rank-One Perturbations of Self-adjoint Operators

“…Rank-one perturbations of matrix pencils and an important eigenvalue placement problem were studied e.g. in [11,19,32], while a more general perturbation theory for structured matrices was outlined in the recent paper [38].…”

Spectra of rank-one perturbations of self-adjoint operators

“…Rank-one perturbations of matrix pencils are discussed e.g. in [9,17,30]. A general perturbation theory for structured matrices is developed in the recent paper [36].…”