The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph

DOI10.1016/j.laa.2016.09.014zbMath1348.05127arXiv1606.05214OpenAlexW2963397771MaRDI QIDQ332633

Polona Oblak, Helena Šmigoc

Publication date: 8 November 2016

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

Full work available at URL: https://arxiv.org/abs/1606.05214

zbMATH Keywords

symmetric matrixminimal rankmultiplicity of an eigenvalue

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (4)

Bordering of symmetric matrices and an application to the minimum number of distinct eigenvalues for the join of graphs ⋮ The liberation set in the inverse eigenvalue problem of a graph ⋮ Corrigendum to: ``Achievable multiplicity partitions in the inverse eigenvalue problem of a graph ⋮ Achievable multiplicity partitions in the inverse eigenvalue problem of a graph

Cites Work

• Unordered multiplicity lists of a class of binary trees
• The inertia set of the join of graphs
• The inverse eigenvalue problem for nonnegative matrices
• The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample
• The minimum rank of symmetric matrices described by a graph: a survey
• Eigenvalues of nonnegative symmetric matrices
• On the possible multiplicities of the eigenvalues of a Hermitian matrix whose graph is a tree
• The implicit construction of multiplicity lists for classes of trees and verification of some conjectures
• Graphs that allow all the eigenvalue multiplicities to be even
• Zero forcing sets and the minimum rank of graphs
• The graphs for which the maximum multiplicity of an eigenvalue is two
• Inertia sets for graphs on six or fewer vertices
• Graphs whose minimal rank is two
• Unordered multiplicity lists of wide double paths
• Minimum number of distinct eigenvalues of graphs

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