The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree

DOI10.1016/j.laa.2018.08.033zbMath1403.15006OpenAlexW2889503206MaRDI QIDQ1794310

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

Publication date: 15 October 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.08.033

zbMATH Keywords

diagonalizable matrixgraph of a matrixsimple eigenvalueeigenvalue multiplicity

Mathematics Subject Classification ID

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

Related Items (2)

Change in vertex status after removal of another vertex in the general setting ⋮ Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments

Cites Work

• Unnamed Item
• Questions, conjectures, and data about multiplicity lists for trees
• Spectral multiplicity and splitting results for a class of qualitative matrices
• Converse to the Parter--Wiener theorem: the case of non-trees
• Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree
• Combinatorially symmetric matrices
• Geometric Parter-Wiener, etc. theory
• On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph
• Diameter minimal 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
• On the Eigenvalues and Eigenvectors of a Class of Matrices

This page was built for publication: The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree