Abstract.
A sign pattern matrix is a matrix whose entries are from the set {+,−,0}. The purpose of this paper is to obtain bounds on the minimum rank of any symmetric sign pattern matrix A whose graph is a tree T (possibly with loops). In the special case when A is nonnegative with positive diagonal and the graph of A is “star-like”, the exact value of the minimum rank of A is obtained. As a result, it is shown that the gap between the symmetric minimal and maximal ranks can be arbitrarily large for a symmetric tree sign pattern A.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by NSF grant No. DMS-00700
AMS classification: 05C50, 05C05, 15A48
Rights and permissions
About this article
Cite this article
Chen, G., Hall, F., Li, Z. et al. On Ranks of Matrices Associated with Trees. Graphs and Combinatorics 19, 323–334 (2003). https://doi.org/10.1007/s00373-002-0522-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s00373-002-0522-8