Further generalization of symmetric multiplicity theory to the geometric case over a field

Isaac Cinzori; Charles R. Johnson; Hannah Lang; Carlos M. Saiago

doi:10.1515/spma-2020-0119

Further generalization of symmetric multiplicity theory to the geometric case over a field

Isaac Cinzori, Charles R. Johnson, Hannah Lang, Carlos M. Saiago

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Abstract

Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.

Original language	English
Pages (from-to)	31-35
Number of pages	5
Journal	special matrices
Volume	9
Issue number	1
DOIs	https://doi.org/10.1515/spma-2020-0119
Publication status	Published - 1 Jan 2021

Keywords

Combinatorially symmetric matrix
Eigenvalue
Generalized star
Geometric multiplicity
Graph of a matrix
Path

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10.1515/spma-2020-0119Licence: CC BY

Further generalization of symmetric multiplicity theory to the geometric case over a fieldFinal published version, 335 KBLicence: CC BY

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AB - Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.

KW - Combinatorially symmetric matrix

KW - Eigenvalue

KW - Generalized star

KW - Geometric multiplicity

KW - Graph of a matrix

KW - Path

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Further generalization of symmetric multiplicity theory to the geometric case over a field

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