The general matrix pencil completion problem: A minimal case

Abstract

In this paper we resolve a classical, long-standing open general matrix pencil completion problem in a minimal case. The problem consists of describing the possible Kronecker invariants of a pencil with a prescribed subpencil, and the restriction we impose is not structural but is only on the number of added rows and columns. We completely resolve the problem in the case when the numbers of added rows and columns are the minimal possible, such that the resulting pencil can have the prescribed number of row and column minimal indices.