We solve the open problem of describing the possible Kronecker invariants of quasi-regular
matrix pencils under bounded rank perturbations. By a quasi-regular matrix pencil we mean …

A square matrix $ A $ has the usual Jordan canonical form that describes the structure of $ A
$ via eigenvalues and the corresponding Jordan blocks. If $ A $ is a linear relation in a finite …

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The change of the Kronecker structure of a matrix pencil perturbed by another pencil of rank
one has been characterized in terms of the homogeneous invariant factors and the chains of …

The relation between the spectra of operator pencils with unbounded coefficients and of
associated linear relations is investigated. It turns out that various types of spectrum coincide …

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) …

Given two linear relations S and T in C n, we characterize when there exist linear relations
S˜ and T˜ in C n, strictly equivalent to S and T, respectively, such that S˜ and T˜ are one …

In this paper, we solve the bounded rank perturbation problem for matrix pencils without
nontrivial homogeneous invariant factors, over arbitrary fields. The solution is based on …

In this paper, we use subsets of the Riemann sphere and specific types of invariant linear
subspaces to introduce the extended spectral decomposable multivalued linear operators …

This paper is devoted to study the interrelations between inessential, improjective, strictly
singular and strictly cosingular linear relations. First, we show that the classes of strictly …