Article
Minimum Rank of Matrices Described by a Graph or Pattern over the Rational, Real and Complex Numbers
Electronic Journal of Combinatorics
Document Type
Article
Disciplines
Publication Version
Published Version
Publication Date
1-1-2008
Abstract
We use a technique based on matroids to construct two nonzero patterns Z1 and Z2 such that the minimum rank of matrices described by Z1 is less over the complex numbers than over the real numbers, and the minimum rank of matrices described by Z2 is less over the real numbers than over the rational numbers. The latter example provides a counterexample to a conjecture in [AHKLR] about rational realization of minimum rank of sign patterns. Using Z1 and Z2, we construct symmetric patterns, equivalent to graphs G1 and G2, with the analogous minimum rank properties. We also discuss issues of computational complexity related to minimum rank.
Copyright Owner
The Authors
Copyright Date
2008
Language
en
File Format
application/pdf
Citation Information
Avi Berman, Shmuel Friedland, Leslie Hogben, Uriel G. Rothblum, et al.. "Minimum Rank of Matrices Described by a Graph or Pattern over the Rational, Real and Complex Numbers" Electronic Journal of Combinatorics Vol. 15 (2008) Available at: http://works.bepress.com/leslie-hogben/54/
This is an article from the Electronic Journal of Combinatorics 15 (2008).