East Asian J. Appl. Math., 4 (2014), pp. 205-221.
Published online: 2018-02
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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} }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.