Elliptic matrices and their eigenpolynomials
type: Item
instance of: scholarly article
title: Elliptic matrices and their eigenpolynomials
zbMATH Open document ID: 0902.15018
DOI: 10.1016/S0024-3795(96)00310-2
author: Xuerong Yong
author: Zheng Wang
published in: Linear Algebra and its Applications
publication date: 1998-12-03T00:00:00Z
review text: A real symmetric matrix is called elliptic if it has exactly one, simple positive eigenvalue. Elliptic matrices with all diagonal entries equal to zero are called `special' and have been discussed by \textit{M. Fiedler} [Linear Algebra Appl. 197-198, 337-347 (1994; Zbl 0799.15013)]. The author investigates the principal submatrices and the eigenpolynomials of elliptic matrices. As an application a simple proof is given for the following result due to J. H. Smith: A simple graph of order \(n\) is completely \(k\)-partite if, and only if, it is a simply connected graph with elliptic adjacency matrix of rank \(k\).
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1044244
zbMATH Keywords: elliptic matrix
zbMATH Keywords: positive eigenvalue
zbMATH Keywords: eigenpolynomials
zbMATH Keywords: simple graph
zbMATH Keywords: connected graph
zbMATH Keywords: elliptic adjacency matrix
reviewed by: Hans Havlicek
MaRDI profile type: Publication
cites work: Elliptic matrices with zero diagonal
cites work: Q5645344
cites work: Q3943082
cites work: Q3907599
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description: scientific article; zbMATH DE number 1044244