TY - JOUR
T1 - Pseudo-Tournament Matrices and Their Eigenvalues
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, eigenvalue, spectral radius, tournament matrix.
AB - <p style="text-align: justify;">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.</p>