A regular matrix pencil sE-A and its rank one perturbations are considered. We determine
the sets in C∪{∞\} which are the eigenvalues of the perturbed pencil. We show that the …

Let P(λ)=A_0+λA_1 be a singular m*n matrix pencil without full rank whose Kronecker
canonical form (KCF) is given. Let ρ be a positive integer such that ρ≦\min{m,n\}-\rmrank(P) …

We describe the generic change of the partial multiplicities at a given eigenvalue \lambda_0
of a regular matrix pencil A_0+λA_1 under perturbations with low normal rank. More …

Classes of regular, structured matrix pencils are examined with respect to their spectral
behavior under a certain type of structure-preserving rank-1 perturbations. The observed …

Rank One Perturbations of Matrix Pencils Page 1 Copyright © by SIAM. Unauthorized reproduction
of this article is prohibited. SIAM J. MATRIX ANAL. APPL. © 2020 Society for Industrial and …

We show that the set of m× m complex skew-symmetric matrix polynomials of even grade d,
ie, of degree at most d, and (normal) rank at most 2r is the closure of the single set of matrix …

We elaborate on the deviation of the Jordan structures of two linear relations that are finite-
dimensional perturbations of each other. We compare their number of Jordan chains of …

Structure-preserving generic low-rank perturbations are studied for classes of structured
matrix pencils, including real symmetric, complex symmetric, and complex Hermitian pencils …

We study the perturbation theory of structured matrices under structured rank one
perturbations, with emphasis on matrices that are unitary, orthogonal, or symplectic with …

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.