Implicit construction of multiple eigenvalues for trees

DOI10.1080/03081080701852756zbMath1176.15011OpenAlexW2043670863MaRDI QIDQ3633151

Brian D. Sutton, Charles R. Johnson, Andrew J. Witt

Publication date: 17 June 2009

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

Full work available at URL: https://doi.org/10.1080/03081080701852756

zbMATH Keywords

treegraphmultiplicityeigenvaluesvinereal symmetric matrix

Mathematics Subject Classification ID

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

Related Items (max. 100)

The change in eigenvalue multiplicity associated with perturbation of a diagonal entry ⋮ Ordered multiplicity lists for eigenvalues of symmetric matrices whose graph is a linear tree ⋮ The implicit construction of multiplicity lists for classes of trees and verification of some conjectures ⋮ Numerical construction of structured matrices with given eigenvalues ⋮ Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments ⋮ The inverse eigenvalue problem for linear trees ⋮ The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a nonlinear tree

Cites Work

• Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: The case of generalized stars and double generalized stars.
• On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• On the Eigenvalues and Eigenvectors of a Class of Matrices

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