Pseudo-Tournament Matrices and Their Eigenvalues

Pseudo-Tournament Matrices and Their Eigenvalues

Year:    2014

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 205–221

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.110213.030414a

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 205–221

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Pseudo-tournament matrix eigenvalue spectral radius tournament matrix.