Acyclic matrices with a small number of distinct eigenvalues

Reshmi Nair; Bryan L. Shader

doi:10.1016/j.laa.2012.08.029

Acyclic matrices with a small number of distinct eigenvalues

Reshmi Nair, Bryan L. Shader

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Spectral properties of the set of all symmetric matrices whose graph is a given tree T are further studied. A new technique based on Smith Normal Form and Hamming Distance is introduced and used to characterize such matrices that have at most four distinct eigenvalues and such matrices that have at most two multiple eigenvalues and whose sum of multiplicities is the maximum possible.

Original language	English (US)
Pages (from-to)	4075-4089
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	10
DOIs	https://doi.org/10.1016/j.laa.2012.08.029
State	Published - May 15 2013
Externally published	Yes

Keywords

Acyclic matrix
Diameter
Hamming distance
Maximum multiplicity
Smith normal form

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2012.08.029

Cite this

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title = "Acyclic matrices with a small number of distinct eigenvalues",

abstract = "Spectral properties of the set of all symmetric matrices whose graph is a given tree T are further studied. A new technique based on Smith Normal Form and Hamming Distance is introduced and used to characterize such matrices that have at most four distinct eigenvalues and such matrices that have at most two multiple eigenvalues and whose sum of multiplicities is the maximum possible.",

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AU - Shader, Bryan L.

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AB - Spectral properties of the set of all symmetric matrices whose graph is a given tree T are further studied. A new technique based on Smith Normal Form and Hamming Distance is introduced and used to characterize such matrices that have at most four distinct eigenvalues and such matrices that have at most two multiple eigenvalues and whose sum of multiplicities is the maximum possible.

KW - Acyclic matrix

KW - Diameter

KW - Hamming distance

KW - Maximum multiplicity

KW - Smith normal form

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EP - 4089

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 10

ER -

Acyclic matrices with a small number of distinct eigenvalues

Abstract

Keywords

ASJC Scopus subject areas

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