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Lower Bounds in Minimum Rank Problems

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
432
Issue
1
Identifiers
DOI: 10.1016/j.laa.2009.08.023
Keywords
  • Minimum Rank
  • Minimum Semidefinite Rank
  • Zero Forcing Set

Abstract

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.

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