The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a nonlinear tree

DOI10.1515/spma-2021-0158zbMath1489.15017OpenAlexW4210768082MaRDI QIDQ2076168

Yanyan Li

Publication date: 18 February 2022

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

Full work available at URL: https://doi.org/10.1515/spma-2021-0158

zbMATH Keywords

eigenvaluegraph of a matrixmultiplicity listnonlinear tree

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)

Uses Software

• OEIS

Cites Work

• Questions, conjectures, and data about multiplicity lists for trees
• Ordered multiplicity lists for eigenvalues of symmetric matrices whose graph is a linear tree
• Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree
• 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.
• The inverse eigenvalue problem for linear trees
• The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a linear tree
• Branch duplication for the construction of multiple eigenvalues in an Hermitian matrix whose graph is a tree
• Implicit construction of multiple eigenvalues for trees
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree
• Eigenvalues, Multiplicities and Graphs

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