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.
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.
Copyright Date
2009
Language
en
File Format
application/pdf
Recommended Citation
Allison, Mary; Bodine, Elizabeth; DeAlba, Luz Maria; Debnath, Joyati; DeLoss, Laura; Garnett, Colin; Grout, Jason; Hogben, Leslie; Im, Bokhee; Kim, Hana; Nair, Reshmi; Pryporova, Olga; Savage, Kendrick; Shader, Bryan; and Wangsness Wehe, Amy, "Minimum rank of skew-symmetric matrices described by a graph" (2010). Mathematics Publications. 96.
https://lib.dr.iastate.edu/math_pubs/96
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.