On the Minimum Rank among Positive Semidefinite Matrices with a Given Graph

Authors

Mathew Booth
Philip Hackney
Benjamin Harris
Charles Johnson
Margaret Lay
Lon Mitchell, University of South Florida St. PetersburgFollow
Sivaram Narayan
Amanda Pascoe
Kelly Steinmetz
Brian Sutton
Wendy Wang

SelectedWorks Author Profiles:

Lon Mitchell

Document Type

Article

Publication Date

2008

Abstract

Let P(G) be the set of all positive semidefinite matrices whose graph is G, and msr(G) be the minimum rank of all matrices in P(G). Upper and lower bounds for msr(G) are given and used to determine msr(G) for some well-known graphs, including chordal graphs, and for all simple graphs on less than seven vertices.

Publisher

Society for Industrial and Applied Mathematics

Recommended Citation

Booth, M., Hackney, P., Harris, B., Johnson, C., Lay, M., Mitchell, L., Narayan, S., Pascoe, A., Steinmetz, K., Sutton, B., & Wang, W. (2008). On the minimum rank among positive semidefinite matrices with a given graph. SIAM Journal on Matrix and Analysis and Applications, 30(2), 731-740. https://doi.org/10.1137/050629793.