On almost regular tournament matrices

被引：8

作者：

Eschenbach, C

Hall, F

Hemasinha, R

Kirkland, SJ

Li, ZS

Shader, BL

Stuart, JL

Weaver, JR ^{[1
]}

机构：

[1] Univ W Florida, Dept Math & Stat, Pensacola, FL 32514 USA

[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

[3] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

[4] Univ Wyoming, Dept Math, Laramie, WY 82071 USA

[5] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 306卷 / 1-3期

关键词：

almost regular tournament; Brualdi-Li conjecture; determinant; eigenvalues; spectral radius; tournament;

D O I：

10.1016/S0024-3795(99)00249-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Spectral and determinantal properties of a special dass M-n of 2n x 2n almost regular tournament matrices are studied. In particular, the maximum Perron value of the matrices in this class is determined and shown to be achieved by the Brualdi-Li matrix, which has been conjectured to have the largest Perron value among all tournament matrices of even order. We also establish some determinantal inequalities for matrices in M-n and describe the structure of their associated walk spaces. (C) 2000 Elsevier Science Inc. All rights reserved.

引用

页码：103 / 121

页数：19

共 19 条

[1]

Algorithms E., 1992, ANN DISCRETE MATH, V53, P221, DOI DOI 10.1016/S0167-5060(08)70325-X

[2]

BRAUER A, 1968, B AM MATH SOC, V74, P1133, DOI 10.1090/S0002-9904-1968-12079-8

[3]

BRAUER A, 1972, LINEAR ALGEBRA APPL, V5, P311

[4]

Brualdi R. A., 1983, DISCRETE MATH, V43, P1133

[5]

Brualdi R. A., 1991, COMBINATORIAL MATRIX, V39

[6] ALGEBRAIC MULTIPLICITY OF THE EIGENVALUES OF A TOURNAMENT MATRIX [J].

DECAEN, D ;

GREGORY, DA ;

KIRKLAND, SJ ;

PULLMAN, NJ ;

MAYBEE, JS .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 169 :179-193

[7]

FRIEDLAND S, 1993, IMA VOL MATH APPL, V50, P189

[8]

Horn R. A., 1986, Matrix analysis

[9]

Kirkland S, 1997, LINEAR ALGEBRA APPL, V262, P209

[10] A note on Perron vectors for almost regular tournament matrices [J].

Kirkland, S .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 266 :43-47

← 1 2 →