Minimal completion problem for quasi-regular matrix pencils

Abstract

In this paper we study the problem of completion of an arbitrary matrix pencil by rows and columns in order to obtain a quasi-regular matrix pencil, in the case when the number of added columns, or rows, is the minimal possible to obtain a quasi-regular matrix pencil. In the solution we use combinatorial methods involving LR coefficients, a solution of the Carlson problem and localization techniques. The result is given over algebraically closed fields.