Matrix pencils completions under double rank restrictions

Abstract

In this paper we study the General Matrix Pencil Completion Problem under double rank restrictions. Considered rank restrictions are not structural, hence the obtained results deal with full sets of Kronecker invariants of the involved matrix pencils, and they generalize many of the existing results in the literature, for example [1,5,7,9,11,12,21,24,45,46].
Main methods consist of combining the celebrated Sa-Thompson's result [1,39,44] with novel results on rank restrictions in completions of matrix pencils. All of the obtained results are explicit and constructive.