Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns

DOI10.1016/j.laa.2006.02.018zbMath1106.05059OpenAlexW2143735454MaRDI QIDQ855530

Timothy L. Hardy, Luz Maria DeAlba, Amy Wangsness, Irvin Roy Hentzel, Leslie Hogben

Publication date: 7 December 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2006.02.018

zbMATH Keywords

sign pattern matrixmaximum multiplicity

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Graph algorithms (graph-theoretic aspects) (05C85)

Related Items (max. 100)

Essential sign change numbers of full sign pattern matrices ⋮ Minimum rank problems ⋮ Rational realization of maximum eigenvalue multiplicity of symmetric tree sign patterns ⋮ A new lower bound for the positive semidefinite minimum rank of a graph ⋮ Zero forcing for sign patterns ⋮ On the minimum semidefinite rank of a simple graph ⋮ The inverse eigenvalue problem of a graph: multiplicities and minors ⋮ An upper bound for the minimum rank of a graph ⋮ The minimum rank of symmetric matrices described by a graph: a survey

Cites Work

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• Ranks of zero patterns and sign patterns^*
• The Parter--Wiener Theorem: Refinement and Generalization
• Graphs whose minimal rank is two
• A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs
• On the Eigenvalues and Eigenvectors of a Class of Matrices
• Symmetric sign pattern matrices that require unique inertia

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