Authors: Dodig, Marija 
Title: Completion of quasi-regular matrix pencils
Journal: Linear Algebra and Its Applications
Volume: 501
First page: 198
Last page: 241
Issue Date: 15-Jul-2016
Rank: M21
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.03.020
Abstract: 
In this paper we give solutions for two important particular cases of the general completion problem, involving quasi-regular matrix pencil. We describe the possible Kronecker invariants of a quasi-regular pencil whose subpencil is prescribed in the case when the prescribed subpencil is without nontrivial homogeneous invariant factors. Also, we solve "the dual problem" by describing the possible Kronecker invariants of a pencil without nontrivial homogeneous invariant factors when a quasi-regular subpencil is prescribed. These two results are expected to be the crucial steps toward a solution of the general completion problem. The results are given over algebraically closed fields.
Keywords: Completion of matrix pencils | Partitions of integers | Polynomial paths | Quasi-regular matrix pencils
Publisher: Elsevier
Project: FCT, project ISFL-1-1431
Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 

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