The change in eigenvalue multiplicity associated with perturbation of a diagonal entry

DOI10.1080/03081087.2011.610973zbMath1247.15007OpenAlexW2043872669MaRDI QIDQ2895696

Charles R. Johnson, Carlos M. Saiago, António Leal-Duarte

Publication date: 4 July 2012

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

Full work available at URL: https://doi.org/10.1080/03081087.2011.610973

zbMATH Keywords

graphHermitian matriceseigenvalue multiplicitysubmatrices

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 (7)

Multiplicities: Adding a Vertex to a Graph ⋮ Changes in vertex status and the fundamental decomposition of a tree relative to a multiple (parter) eigenvalue ⋮ The effect of perturbation of an off-diagonal entry pair on the geometric multiplicity of an eigenvalue ⋮ 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 ⋮ 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 ⋮ The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

Cites Work

• Spectral multiplicity and splitting results for a class of qualitative matrices
• Converse to the Parter--Wiener theorem: the case of non-trees
• On Fiedler- and Parter-vertices of acyclic matrices
• The structure of matrices with a maximum multiplicity eigenvalue
• Matrices with prescribed characteristic polynomials and a prescribed submatrix. I, II
• Branch duplication for the construction of multiple eigenvalues in an Hermitian matrix whose graph is a tree
• Implicit construction of multiple eigenvalues for trees
• Matrix Analysis
• 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
• Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors
• On the Eigenvalues and Eigenvectors of a Class of Matrices

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