The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree
Rosário Fernandes
Special Matrices, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:268700 
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     author = {Ros\'ario Fernandes},
     title = {The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree},
     journal = {Special Matrices},
     volume = {3},
     year = {2015},
     zbl = {1310.15016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0001}
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Rosário Fernandes. The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0001/

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