The classification of edges and the change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the change in an edge value

DOI10.1515/spma-2017-0004zbMath1360.15014OpenAlexW2581782472MaRDI QIDQ516666

Kenji Toyonaga, Charles R. Johnson

Publication date: 15 March 2017

Published in: Special Matrices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/spma-2017-0004

zbMATH Keywords

treegraphmultiplicityedgeseigenvaluesreal symmetric matrixmatrix entries

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (7)

The change in multiplicity of an eigenvalue due to adding or removing edges ⋮ The effect of removing a 2-downer edge or a cut 2-downer edge triangle for an eigenvalue ⋮ The effect of perturbation of an off-diagonal entry pair on the geometric multiplicity of an eigenvalue ⋮ The change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the changes in edge values around a classified vertex in a tree ⋮ Classification of vertices and edges with respect to the geometric multiplicity of an eigenvalue in a matrix, with a given graph, over a field ⋮ Classification of edges in a general graph associated with the change in multiplicity of an eigenvalue ⋮ The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

Cites Work

• The change in multiplicity of an eigenvalue of a Hermitian matrix associated with the removal of an edge from its graph
• Spectral multiplicity and splitting results for a class of qualitative matrices
• The change in eigenvalue multiplicity associated with perturbation of a diagonal entry
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• Hermitian Matrices, Eigenvalue Multiplicities, and Eigenvector Components
• On the Eigenvalues and Eigenvectors of a Class of Matrices
• Unnamed Item

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