Completion of matrix pencils with a single rank restriction

Abstract

In this paper we consider and solve the General Matrix Pencil Completion Problem (GMPCP) under single rank restrictions. These constraints are less limiting than any other restrictions on the GMPCP studied in the past. Thus, the obtained results directly generalize the existing results in the literature on the GMPCP. Finally, as one direct corollary of the main results, we obtain a novel result on determining the possible Kronecker invariants of a quasi-regular matrix pencil with a prescribed subpencil.