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

โœ Scribed by Booth, Matthew; Hackney, Philip; Harris, Benjamin; Johnson, Charles R.; Lay, Margaret; Mitchell, Lon H.; Narayan, Sivaram K.; Pascoe, Amanda; Steinmetz, Kelly; Sutton, Brian D.; Wang, Wendy


Book ID
118215886
Publisher
Society for Industrial and Applied Mathematics
Year
2008
Tongue
English
Weight
152 KB
Volume
30
Category
Article
ISSN
0895-4798

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โœ Liang-Hao Huang; Gerard J. Chang; Hong-Gwa Yeh ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 164 KB

For a simple graph G on n vertices, the minimum rank of G over a field F, written as mr F (G), is defined to be the smallest possible rank among all n ร— n symmetric matrices over F whose (i, j)th entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A symmetric integ