Combinatorial Analysis of Kronecker Canonical Forms of Matrix Pencils

Abstract

The Kronecker canonical form of matrix pencils plays an important role in various fields such as systems control and differential-algebraic equations. The Kronecker canonical form admits two characterizations: the highest degree of subdeterminants, which can be computed by combinatorial relaxation algorithms, and the ranks of larger constant matrices called expanded matrices. This article surveys the combinatorial approach to the analysis of the Kronecker canonical form.