Further generalization of symmetric multiplicity theory to the geometric case over a field-Reference-Cited by-同舟云学术

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

Published:2021-01-01 Issue:1 Volume:9 Page:31-35
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Cinzori Isaac¹,Johnson Charles R.²,Lang Hannah³,Saiago Carlos M.⁴

Affiliation:

1. Department of Mathematics , Michigan State University , East Lansing, MI, 48824, USA .

2. Department of Mathematics , College of William and Mary , P.O. Box 8795, Williamsburg, VA 23187-8795, USA .

3. Department of Mathematics , Harvard University , Cambridge , MA, 02138, USA .

4. Centro de Matematica e Aplicacoes (CMA/FCT/UNL), Departamento de Matematica , Faculdade de Ciencias e Technologia da Universidade NOVA de Lisboa , 2829-516 Quinta da Torre , Portugal .

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2020-0119/pdf

Reference7 articles.

1. [1] C.R. Johnson and A. Leal-Duarte. The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree. Linear and Multilinear Algebra 46:139–144 (1999).

2. [2] C.R. Johnson, A. Leal-Duarte, and C.M. Saiago. The Parter-Wiener theorem: refinement and generalization. SIAM Journal on Matrix Analysis and Applications 25(2):352–361 (2003).

3. [3] C.R. Johnson, A. Leal-Duarte, and C.M. Saiago. 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. Linear Algebra and its Applications 373:311-330 (2003).

4. [4] A. Mohammadian. Trees and acyclic matrices over arbitrary fields. Linear and Multilinear Algebra 64(3):466-476 (2016).

5. [5] C.R. Johnson, C.M. Saiago. Geometric Parter–Wiener, etc. theory. Linear Algebra and Its Applications 537:332-347 (2018).