| Institution: | (1) Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA;(2) Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA;(3) Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA;(4) Department of Mathematics, University of Mississippi, University, MS 38677, USA |
| 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.
Supported by NSF grant No. DMS-00700AMS classification: 05C50, 05C05, 15A48 |
