On the minimum semidefinite rank of a simple graph

Matthew Booth, Philip Hackney, Benjamin Harris, Charles R. Johnson, Margaret Lay, Terry D. Lenker, Lon H. Mitchell, Sivaram K. Narayan, Amanda Pascoe, Brian D. Sutton

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The minimum semidefinite rank (msr) of a graph is defined to be the minimum rank among all positive semidefinite matrices whose zero/ nonzero pattern corresponds to that graph. We recall some known facts and present new results, including results concerning the effects of vertex or edge removal from a graph on msr.

Original languageEnglish
Pages (from-to)483-506
Number of pages24
JournalLinear and Multilinear Algebra
Issue number5
StatePublished - May 2011


  • Graph of a matrix
  • Positive semidefinite
  • Rank
  • Vector representation


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