S
Shaun M. Fallat
Researcher at University of Regina
Publications - 125
Citations - 3202
Shaun M. Fallat is an academic researcher from University of Regina. The author has contributed to research in topics: Matrix (mathematics) & Eigenvalues and eigenvectors. The author has an hindex of 27, co-authored 110 publications receiving 2815 citations. Previous affiliations of Shaun M. Fallat include College of William & Mary.
Papers
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Journal ArticleDOI
Zero forcing sets and the minimum rank of graphs
Francesco Barioli,Wayne Barrett,Steve Butler,Sebastian M. Cioabă,Dragoš Cvetković,Shaun M. Fallat,Chris Godsil,Willem H. Haemers,Leslie Hogben,Rana Mikkelson,Sivaram K. Narayan,Olga Pryporova,Irene Sciriha,Wasin So,Dragan Stevanović,Hein van der Holst,Kevin N. Vander Meulen,Amy Wangsness Wehe +17 more
TL;DR: In this article, the minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i 6 j) is nonzero whenever {i,j} is an edge in G and is zero otherwise.
Journal ArticleDOI
The minimum rank of symmetric matrices described by a graph: A survey☆
Shaun M. Fallat,Leslie Hogben +1 more
TL;DR: The current state of knowledge on the problem of determining the minimum rank of a graph and related issues is surveyed.
Book
Totally Nonnegative Matrices
TL;DR: A comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants, can be found in this article.
Journal ArticleDOI
Zero forcing parameters and minimum rank problems
Francesco Barioli,Wayne Barrett,Shaun M. Fallat,H. Tracy Hall,Leslie Hogben,Leslie Hogben,Bryan L. Shader,P. van den Driessche,Hein van der Holst +8 more
TL;DR: In this paper, the positive semidefinite zero forcing number Z(G) is introduced, which is the minimum number of vertices in a zero forcing set of a graph G, used to study the maximum nullity/minimum rank of the family of symmetric matrices described by G.
Posted Content
Zero forcing parameters and minimum rank problems
Francesco Barioli,Wayne Barrett,Shaun M. Fallat,H. Tracy Hall,Leslie Hogben,Leslie Hogben,Bryan L. Shader,P. van den Driessche,Hein van der Holst +8 more
TL;DR: In this article, the positive semidefinite zero forcing number (Z_+(G) ) is introduced, and shown to be equal to |G|-OS(G), where OS(G) is the recently defined ordered set number that is a lower bound for minimum positive semi-definite rank.