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 −.
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.
Copyright Date
2010
Language
en
File Format
application/pdf
Recommended Citation
Hogben, Leslie and McLeod, Jillian, "A linear algebraic view of partition regular matrices" (2010). Mathematics Publications. 66.
https://lib.dr.iastate.edu/math_pubs/66
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.