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Tytuł artykułu

The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree

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Języki publikacji
EN
Abstrakty
EN
The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2. Using a combinatorial algorithm, cases of equality are computed for M2.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2014-09-10
zaakceptowano
2014-12-04
online
2015-01-12
Twórcy
  • Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade
    Nova de Lisboa, 2829-516 Caparica, Portugal
Bibliografia
  • [1] R. Fernandes, On the inverse eigenvalue problems: the case of superstars. Electronic Journal of Linear Algebra 18 (2009),442-461.
  • [2] R. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press New York (1985).
  • [3] C.R. Johnson and A.Leal Duarte, The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, Linear andMultilinear Algebra 46 (1999), 139-144.
  • [4] C.R. Johnson and A.Leal Duarte, On the possible multiplicities of the eigenvalues of a Hermitian matrix whose graph is atree, Linear Algebra and Applications 248 (2002), 7-21.
  • [5] C.R. Johnson, A.Leal Duarte and C.M. Saiago, The Parter-Wiener theorem: refinement and generalization, SIAM Journalon Matrix Analysis and Applications 25 (2) (2003), 352-361.[Crossref]
  • [6] C.R. Johnson, A.Leal Duarte and C.M. Saiago, Inverse eigenvalue problems and lists of multiplicities of eigenvalues formatrices whose graph is a tree: The case of generalized stars and double generalized stars, Linear Algebra and its Applications373 (2003), 311-330.
  • [7] C.R. Johnson, C. Jordan-Squire and D.A. Sher, Eigenvalue assignments and the two largest multiplicities in a Hermitianmatrix whose graph is a tree, Discrete Applied Mathematics 158 (2010), 681-691.[WoS]
  • [8] S. Parter, On the eigenvalues and eigenvectors of a class of matrices, Journal of the Society for Industrial and AppliedMathematics 8 (1960), 376-388.
  • [9] G.Wiener, Spectral multiplicity and splitting results for a class of qualitativematrices, Linear Algebra and its Applications61 (1984), 15-18.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0001
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