Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

5-2010

Journal or Book Title

Linear Algebra and its Applications

Volume

432

DOI

10.1016/j.laa.2009.10.001

Abstract

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.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 432 (2010): 2457, doi:10.1016/j.laa.2009.10.001. Posted with permission.

Rights

This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

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