[BOOK][B] Handbook of linear algebra

L Hogben - 2006 - books.google.com
The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

Zero forcing parameters and minimum rank problems

F Barioli, W Barrett, SM Fallat, HT Hall… - Linear Algebra and its …, 2010 - Elsevier
The zero forcing number Z (G), which is the minimum number of vertices in a zero forcing set
of a graph G, is used to study the maximum nullity/minimum rank of the family of symmetric …

[BOOK][B] Inverse problems and zero forcing for graphs

L Hogben, JCH Lin, BL Shader - 2022 - books.google.com
This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$ G $)
and the related area of zero forcing, propagation, and throttling. The IEP-$ G $ grew from the …

Variants on the minimum rank problem: A survey II

S Fallat, L Hogben - arxiv preprint arxiv:1102.5142, 2011 - arxiv.org
The minimum rank problem for a (simple) graph $ G $ is to determine the smallest possible
rank over all real symmetric matrices whose $ ij $ th entry (for $ i\neq j $) is nonzero …

Positive semidefinite zero forcing

J Ekstrand, C Erickson, HT Hall, D Hay… - Linear Algebra and its …, 2013 - Elsevier
The positive semidefinite zero forcing number Z+(G) of a graph G was introduced in Barioli
et al.(2010)[4]. We establish a variety of properties of Z+(G): Any vertex of G can be in a …

[BOOK][B] Positive semidefinite maximum nullity and zero forcing number

TA Peters - 2012 - search.proquest.com
The zero forcing number is used to study the maximum nullity/minimum rank of the family of
symmetric matrices described by a simple, undirected graph. We study the positive …

[PDF][PDF] Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees

J Ekstrand, C Erickson, D Hay… - The Electronic Journal …, 2012 - journals.uwyo.edu
The maximum positive semidefinite nullity of a multigraph G is the largest possible nullity
over all real positive semidefinite matrices whose (i, j) th entry (for i= j) is zero if i and j are …

Frame graph

F Abdollahi, H Najafi - Linear and Multilinear Algebra, 2018 - Taylor & Francis
Let be a finite-dimensional Hilbert space and be a finite frame for. For, we associate a simple
graph denoted by and called frame graph, with all elements of as vertices, and two distinct …

Inertia sets for graphs on six or fewer vertices

W Barrett, C Jepsen, R Lang, E McHenry… - … Electronic Journal of …, 2010 - journals.uwyo.edu
Let G be an undirected graph on n vertices and let S (G) be the set of all real symmetric n× n
matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to …

Orthogonal representations, projective rank, and fractional minimum positive semidefinite rank: Connections and new directions

L Hogben, KF Palmowski, DE Roberson… - arxiv preprint arxiv …, 2015 - arxiv.org
Fractional minimum positive semidefinite rank is defined from $ r $-fold faithful orthogonal
representations and it is shown that the projective rank of any graph equals the fractional …