ON TOURNAMENT MATRICES

被引：11
|
作者：
SHADER, BL [1 ]
机构：
[1] UNIV WISCONSIN,DEPT MATH,MADISON,WI 53706
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 1992年 / 162卷
关键词：
D O I：
10.1016/0024-3795(92)90384-M
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let T be a tournament of order n with adjacency matrix M. We find several conditions that are equivalent to M being singular. A correlation between the number of 3-cycles in T and the rank of M is established. It is shown that asymptotically at least 1/2 of the tournament matrices are nonsingular. We also derive bounds on the spectral radius of tournament matrices with a given row-sum vector,
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页码：335 / 368
页数：34
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