The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree
type: Item
instance of: scholarly article
title: The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree
zbMATH Open document ID: 1403.15006
author: Charles R. Johnson
author: António Leal Duarte
author: Carlos M. Saiago
published in: Linear Algebra and its Applications
publication date: 2018-10-15T00:00:00Z
review text: The first and the third author [Linear Algebra Appl. 537, 332--347 (2018; Zbl 1376.15030)] recently began to generalize the multiplicity theory for Hermitian matrices and trees to geometric multiplicities of general matrices over a field when the graph is a tree. In the present paper, the authors are interested in the number of eigenvalues of multiplicity 1 in the case of diagonalizable matrices over a general field when the graph is a tree. They give several positive results that show that at least two multiplicity 1 eigenvalues exist if the tree has either a small number of vertices of degree \(\geq 3\) or a small number of \(g\)-Parter vertices or a small diameter, accompanied by examples featuring at most one multiplicity 1 eigenvalue in the opposite cases.
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 6954362
zbMATH Keywords: eigenvalue multiplicity
zbMATH Keywords: simple eigenvalue
zbMATH Keywords: diagonalizable matrix
zbMATH Keywords: graph of a matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2018.08.033
OpenAlex ID: W2889503206
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DOI: 10.1016/J.LAA.2018.08.033
description: scientific article; zbMATH DE number 6954362