The minimum rank problem over finite fields
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 691-716.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: The structure of all graphs having minimum rank at most k over a finite field with q elements is characterized for any possible k and q. A strong connection between this characterization and polarities of projective geometries is explained. Using this connection, a few results in the minimum rank problem are derived by applying some known results from projective geometry.
Classification : 05C50, 05C75, 15A03, 05B25, 51E20
Mots-clés : minimum rank, symmetric matrix, finite field, projective geometry, polarity graph, bilinear symmetric form 
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Grout, Jason. The minimum rank problem over finite fields. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 691-716. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a5/