Regular linear matrix pencils AE∂∈ Kn× n [∂], where K= Q, R or C, and the associated
differential algebraic equation (DAE) Ex˙= Ax are studied. The Wong sequences of …

For a linear relation in a linear space the concepts of ascent, descent, nullity, and defect are
introduced and studied. It is shown that the results of AE Taylor and MA Kaashoek …

We study singular matrix pencils and show that the so-called Wong sequences yield a quasi-
Kronecker form. This form decouples the matrix pencil into an underdetermined part, a …

In the present thesis we consider differential-algebraic equations (DAEs) of the form d dt Ex=
Ax+ f, where E and A are arbitrary matrices. If E has nonzero entries, then derivatives of the …

We show that the Kronecker canonical form (which is a canonical decomposition for pairs of
matrices) is the representation of a linear relation in a finite dimensional space. This …

In this paper one presents a collection of results about the “bar codes” and “Jordan blocks”
introduced in Burghelea and Dey (Discret Comput Geom 50: 69–98 2013) as computer …

Quasi-Fredholm relations of degree d∈ N in Hilbert spaces are defined in terms of
conditions on their ranges and kernels. They are completely characterized in terms of an …

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 …