Volume 4, Issue 3
Pseudo-Tournament Matrices and Their Eigenvalues

Chuanlong Wang & Xuerong Yong

East Asian J. Appl. Math., 4 (2014), pp. 205-221.

Published online: 2018-02

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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

Pseudo-tournament matrix eigenvalue spectral radius tournament matrix

  • AMS Subject Headings

15A15 05C20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-205, author = {Chuanlong Wang and Xuerong Yong}, title = {Pseudo-Tournament Matrices and Their Eigenvalues}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.110213.030414a}, url = {http://global-sci.org/intro/article_detail/eajam/10833.html} }
TY - JOUR T1 - Pseudo-Tournament Matrices and Their Eigenvalues AU - Chuanlong Wang & Xuerong Yong JO - East Asian Journal on Applied Mathematics VL - 3 SP - 205 EP - 221 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.110213.030414a UR - https://global-sci.org/intro/article_detail/eajam/10833.html KW - Pseudo-tournament matrix KW - eigenvalue KW - spectral radius KW - tournament matrix AB -

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.

Chuanlong Wang & Xuerong Yong. (1970). Pseudo-Tournament Matrices and Their Eigenvalues. East Asian Journal on Applied Mathematics. 4 (3). 205-221. doi:10.4208/eajam.110213.030414a
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