This open access book provides a solution theory for time-dependent partial differential
equations, which classically have not been accessible by a unified method. Instead of using …

We consider linear port-Hamiltonian differential-algebraic equations. Inspired by the
geometric approach of van der Schaft and Maschke [System Control Lett., 121 (2018), pp. 31 …

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 …

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 …

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 …

We study matrix pencils s E− A using the associated linear subspace ker⁡[A,− E]. The
distance between subspaces is measured in terms of the gap metric. In particular, we …

Singular chain spaces for linear relations in linear spaces play a fundamental role in the
decomposition of linear relations in finite-dimensional spaces. In this paper singular chains …

For a linear time-invariant system x˙(t)= A x (t)+ B u (t), the Kronecker canonical form (KCF) of
the matrix pencil (s I− A| B) provides the controllability indices, also called column minimal …

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) …