Pseudo-Tournament Matrices and Their Eigenvalues
نویسندگان
چکیده
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. AMS subject classifications: 15A15, 05C20
منابع مشابه
Pseudo - tournament matrices , Brualdi - Li matrices and their new properties ∗
An n × n complex matrix A is h-pseudo-tournament if A + A∗ = hh∗ − I, where h is a complex, non-zero column vector. The class of h-pseudo-tournament matrices is a generalization of the well studied tournament-like matrices: h-hypertournament matrices, generalized tournament matrices and tournament matrices. In this paper we derive new spectral properties of an h-pseudo-tournament matrix. When t...
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