On the possible multiplicities of the eigenvalues of a Hermitian matrix whose graph is a tree
By Charles R. Johnson, António Leal Duarte. 2002
57 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4eb116dcfc07da4da1e181966ab30e35260f3924
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In Computational Theory and Mathematics
In Electrical and Electronic Engineering
In Geometry and Topology
Citations in the corpus
- 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 (2003, background): “We note that the paths and generalized stars are also (degenerate) double generalized stars, as well as the double paths studied in [4].”