Singular, nonsingular, and bounded rank completions of ACI-matrices |
| |
Authors: | Richard A Brualdi |
| |
Institution: | a Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA b Department of Mathematics, East China Normal University, Shanghai 200241, China |
| |
Abstract: | An affine column independent matrix is a matrix whose entries are polynomials of degree at most 1 in a number of indeterminates where no indeterminate appears with a nonzero coefficient in two different columns. A completion is a matrix obtained by giving values to each of the indeterminates. Affine column independent matrices are more general than partial matrices where each entry is either a constant or a distinct indeterminate. We determine when the rank of all completions of an affine column independent matrix is bounded by a given number, generalizing known results for partial matrices. We also characterize the square partial matrices over a field all of whose completions are nonsingular. The maximum number of free entries in such matrices of a given order is determined as well as the partial matrices with this maximum number of free entries. |
| |
Keywords: | 05C50 15A15 15A99 |
本文献已被 ScienceDirect 等数据库收录! |
|