Lower Bounds in Minimum Rank Problems

Lon H. Mitchell, Sivaram K. Narayan, Andrew M. Zimmer

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

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.

Original languageEnglish
Pages (from-to)430-440
Number of pages11
JournalLinear Algebra and Its Applications
Volume432
Issue number1
DOIs
StatePublished - Jan 1 2010

Keywords

  • Minimum rank
  • Minimum semidefinite rank
  • Zero forcing set

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