Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

12-2010

Journal or Book Title

Linear Algebra and its Applications

Volume

433

DOI

10.1016/j.laa.2010.06.041

Abstract

Rado showed that a rational matrix is partition regular over N if and only if it satisfies the columns condition. We investigate linear algebraic properties of the columns condition, especially for oriented (vertex-arc) incidence matrices of directed graphs and for sign pattern matrices. It is established that the oriented incidence matrix of a directed graph Γ has the columns condition if and only if Γ is strongly connected, and in this case an algorithm is presented to find a partition of the columns of the oriented incidence matrix with the maximum number of cells. It is shown that a sign pattern matrix allows the columns condition if and only if each row is either all zeros or the row has both a + and −.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 433 (2010): 1809, doi:10.1016/j.laa.2010.06.041. Posted with permission.

Rights

This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

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