Lower Bounds in Minimum Rank Problems

Lon Mitchell, Sivaram K. Narayan, Andrew Zimmer

Type: Article

Publication Date: 2009-10-02

Citations: 28

DOI: https://doi.org/10.1016/j.laa.2009.08.023

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Locations

Linear Algebra and its Applications - View

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+	Positive semidefinite zero forcing	2013	Jason Ekstrand Craig Erickson H. Tracy Hall Diana Hay Leslie Hogben Ryan Johnson Nicole Kingsley Steven Osborne Travis Peters J. Roat
+	Finding Low-rank Solutions of Sparse Linear Matrix Inequalities using Convex Optimization	2017	Ramtin Madani Somayeh Sojoudi Ghazal Fazelnia Javad Lavaei
+	Zero forcing parameters and minimum rank problems	2010	Francesco Barioli Wayne Barrett Shaun Fallat H. Tracy Hall Leslie Hogben Bryan L. Shader P. van den Driessche Hein van der Holst
+ PDF Chat	Zero forcing parameters and minimum rank problems	2010	Francesco Barioli Wayne Barrett Shaun Fallat H. Tracy Hall Leslie Hogben Bryan L. Shader P. van den Driessche Hein van der Holst
+	A new lower bound for the positive semidefinite minimum rank of a graph	2012	Andrew Zimmer
+	Lower bounds for minimum semidefinite rank from orthogonal removal and chordal supergraphs	2011	Lon Mitchell Sivaram K. Narayan Andrew Zimmer
+	Bounds for minimum semidefinite rank from superpositions and cutsets	2012	Jonathan E. Beagley Lon Mitchell Sivaram K. Narayan Eileen L. Radzwion Sara P. Rimer Rachael Tomasino Jennifer L. Wolfe Andrew Zimmer
+	Frame graph	2017	A. Abdollahi Hashem Najafi
+	Computational Methods for Nonlinear Optimization Problems: Theory and Applications	2015	Ramtin Madani
+ PDF Chat	Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees	2012	Jason Ekstrand Craig Erickson Diana Hay Leslie Hogben J. Roat

Works Cited by This (8)

Action	Title	Year	Authors
+ PDF Chat	Graphs whose minimal rank is two	2004	Wayne Barrett Hein van der Holst Raphael Loewy
+	On the Minimum Rank Among Positive Semidefinite Matrices with a Given Graph	2008	Matthew Booth Philip Hackney Benjamin Harris Charles R. Johnson Margaret Lay Lon Mitchell Sivaram K. Narayan Amanda Pascoe Kelly Steinmetz Brian Sutton
+ PDF Chat	The minimum rank of symmetric matrices described by a graph: A survey	2007	Shaun Fallat Leslie Hogben
+	Linearly independent vertices and minimum semidefinite rank	2009	Philip Hackney Benjamin Harris Margaret Lay Lon Mitchell Sivaram K. Narayan Amanda Pascoe
+	On the Shannon capacity of a graph	1979	László Lovász
+	Vector representations of graphs	1989	T. D. Parsons Tomaž Pisanski
+ PDF Chat	Orthogonal representations and connectivity of graphs	1989	László Lovász Michael Saks Alexander Schrijver
+	Three-connected graphs whose maximum nullity is at most three	2008	Hein van der Holst