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Pseudo-Tournament Matrices and Their Eigenvalues

Published online by Cambridge University Press:  28 May 2015

Chuanlong Wang  and
Xuerong Yong
Chuanlong Wang*
Affiliation:
Department of Mathematics, Taiyuan Normal University, Taiyuan, Shanxi, China
Xuerong Yong*
Affiliation:
Department of Mathematical Sciences, The University of Puerto Rico, Mayaguez, PR 00681, USA
*
Corresponding author. Email address: clwang218@126.net
Corresponding author. Email address: xryong@dimacs.rutgers.edu
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Abstract

A tournament matrix and its corresponding directed graph both arise as a record of the outcomes of a round robin competition. An n × n complex matrix A is called h-pseudo-tournament if there exists a complex or real nonzero column vector h such that A + A* = hh* − I. This class of matrices is a generalisation of well-studied tournament-like matrices such as h-hypertournament matrices, generalised tournament matrices, tournament matrices, and elliptic matrices. We discuss the eigen-properties of an h-pseudo-tournament matrix, and obtain new results when the matrix specialises to one of these tournament-like matrices. Further, several results derived in previous articles prove to be corollaries of those reached here.

Keywords

15A1505C20Pseudo-tournament matrixeigenvaluespectral radiustournament matrix
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 3 , August 2014 , pp. 205 - 221
Copyright
Copyright © Global-Science Press 2014

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