具有四个不同特征值的竞赛矩阵

TOURNAMENT MATRICES WITH EXACTLY FOUR DISTINCT EIGENVALUES

设A是n阶竞赛矩阵,k是非负整数.文犤3犦刻划了恰好有三个不同特征值的n阶竞赛矩阵,文犤4犦刻划了恰好有四个不同特征值并且0作为一个一重特征值的n阶竞赛矩阵.在这篇文章中我们主要研究了两个问题:(1)讨论当k是A的特征值时A的性质.(2)刻划恰好有四个不同特征值并且k作为一个一重特征值的全部n阶竞赛矩阵.

Let A be a tournament matrix of order n and k be a nonnegative integer.characterize the tournament matrices with exactly three distinct eigenvalues,characterize the tournament matrices with exactly four distinct eigenvalues and0as a simple eigenvalue.In this paper,we study two problems:(1)The properties of A are studied when k is an eigen-value of A.(2)The tournament matrices of order n are characterized which have exactly four distince eigenvalues and have0as a simple eigenvalue.