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Minimum rank of skew-symmetric matrices described by a graph

✍ Scribed by IMA-ISU research group on minimum rank

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 337 KB
Volume: 432
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.10.001

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✦ Synopsis

The minimum (symmetric) rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The problem of determining minimum (symmetric) rank has been studied extensively. We define the minimum skew rank of a simple graph G to be the smallest possible rank among all skew-symmetric matrices over F whose ijth entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. We apply techniques from the minimum (symmetric) rank problem and from skew-symmetric matrices to obtain results about the minimum skew rank problem.

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