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On the possible multiplicities of the eigenvalues of a Hermitian matrix whose graph is a tree by Charles R. Johnson; António Leal Duarte is a Mathematics article available to read on EtoBox.

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We consider the general problem of determining which lists of multiplicities for the eigenvalues occur among Hermitian matrices the graph of whose off-diagonal entries is a given tree. Several restrictions are cited and a construction strategy is given. Together, these are sufficient to characterize all lists for each tree in two infinite classes: the double paths and generalized stars, and to tabulate all lists for trees on fewer than nine vertices. Such tables should be useful for formulating and dispelling general conjectures.

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Author

Charles R. Johnson; António Leal Duarte

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0024-3795)

Published

2002

Language

EN

Field

Mathematics (Physical Sciences)