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Multiplicity Lists for Classes of Hermitian Matrices whose Graph is a Certain Tree
McMichael, Paul
McMichael, Paul
Abstract
Given a certain tree, we explore what we can infer about the eigenvalue multiplicities for a Hermitian matrix whose graph is that tree solely from the tree itself. Topics include the minimum number of 1's among the possible multiplicity lists and the effects of edge subdivision and vertex deletion in the tree on the possibly multiplicity lists. We also begin to explore what we can infer about the eigenvalue multiplicity lists of Hermitian matrices whose graph is a certain non-tree from what we already know about trees.
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Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.
Date
2008-05-13
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Keywords
Hermitian matrices, Graph theory, Trees, Linear algebra
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Department
Mathematics