COMBINATORICS OF COLUMN MINIMAL INDICES AND MATRIX PENCIL COMPLETION PROBLEMS

摘要

In this paper we describe the possible Kronecker invariants of a matrix pencil with a prescribed subpencil, when the prescribed subpencil has only column (row) minimal indices as Kronecker invariants. This is done by exploiting combinatorics of column minimal indices and by introducing some novel labels. The result is given over arbitrary fields.