Lower Bounds in Minimum Rank Problems

Authors

Lon Mitchell, University of South Florida St. PetersburgFollow
Sivaram Narayan
Andrew Zimmer

SelectedWorks Author Profiles:

Lon Mitchell

Document Type

Article

Publication Date

2010

ISSN

0024-3795

Abstract

The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the given graph. The minimum semidefinite rank of a graph is the minimum rank among Hermitian positive semidefinite matrices with the given graph. We explore connections between OS-sets and a lower bound for minimum rank related to zero forcing sets as well as exhibit graphs for which the difference between the minimum semidefinite rank and these lower bounds can be arbitrarily large.

Publisher

Elsevier

Recommended Citation

Mitchell, L., Narayan, S. & Zimmer, A. (2010). Lower Bounds in Minimum Rank Problems. Linear Algebra and its Applications, 432(1), 430-440. https://doi.org/10.1016/j.laa.2009.08.023.