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- Luz M. DeAlba, Irvin Roy Hentzel, +5 authors Kevin N. Vander Meulen
- 2006

A sign pattern Z (a matrix whose entries are elements of {+,âˆ’, 0}) is spectrally arbitrary if for any selfconjugate spectrum there is a real matrix with sign pattern Z having the given spectrum.â€¦ (More)

- Francesco Barioli, Wayne Barrett, +5 authors Hein van der Holst
- 2010

Abstract. The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a 1 graph G, is used to study the maximum nullity/minimum rank of the family of symmetricâ€¦ (More)

- Richard A. Brualdi, Leslie Hogben, +27 authors Amy Wangsness
- 2007

The workshop Spectra of Families of Matrices described by Graphs, Digraphs, and Sign Patterns, held at the American Institute of Mathematics Research Conference Center on Oct. 23-27, 2006, focused onâ€¦ (More)

- Carolyn Eschenbach, Frank J. Hall, +5 authors James Weaver
- The American Mathematical Monthly
- 2000

1. TOURNAMENTS. In an n-player round robin tournament, each player plays one match against each of the other n 1 players. The win-loss outcomes of these matches can be conveniently recorded in aâ€¦ (More)

We explore combinatorial matrix patterns of order n for which some matrix entries are necessarily nonzero, some entries are zero, and some are arbitrary. In particular, we are interested in when theâ€¦ (More)

Nearly positive matrices are nonnegative matrices which, when premultiplied by orthogonal matrices as close to the identity as one wishes, become positive. In other words, all columns of a nearlyâ€¦ (More)

For a graph G of order n, the maximum nullity of G is defined to be the largest possible nullity over all real symmetric n Ã— n matrices A whose (i, j)th entry (for i 6= j) is nonzero whenever {i, j}â€¦ (More)

- Shaun M. Fallat, H. Tracy Hall, Daniel, HERSHKOWITZ, Leslie Hogben, Bryan Shader
- 2009

The minimum rank of a directed graph Î“ is defined to be the smallest possible rank over all real matrices whose ijth entry is nonzero whenever (i, j) is an arc in Î“ and is zero otherwise. Theâ€¦ (More)

We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de VerdiÃ¨re-type parameters. Letâ€¦ (More)

For a graph G of order n, the maximum nullity of G is defined to be the largest possible nullity over all real symmetric n Ã— n matrices A whose (i, j)th entry (for i 6= j) is nonzero whenever {i, j}â€¦ (More)