On a conjecture about the eigenvalues of doubly stochastic matrices

被引：15

作者：

Mashreghi, Javad ^{[1
]}

Rivard, Roland ^{[1
]}

机构：

[1] Univ Laval, Dept Math & Stat, Quebec City, PQ G1K 7P4, Canada

来源：

LINEAR & MULTILINEAR ALGEBRA | 2007年 / 55卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

stochastic matrices; doubly stochastic matrices; eigenvalue; spectrum;

D O I：

10.1080/03081080600899296

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

According to a long standing conjecture, the geometric location of eigenvalues of doubly stochastic matrices of order n is exactly the union of regular k- gons anchored at 1 in the unit disc for 2 <= k <= n. It is easy to verify this fact for n = 2, 3. But, for n >= 4, it has been an open question. We show that this conjecture is wrong for n 5.

引用

页码：491 / 498

页数：8

共 9 条

[1]

Dmitriev N, 1945, C R DOKLADY ACAD SCI, V49, P159

[2]

DMITRIEV N., 1946, Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya, V10, P167

[3]

FRITZ FJ, 1979, STOCHASTISCHE MATRIZ

[4]

Ito H, 1997, LINEAR ALGEBRA APPL, V267, P241, DOI 10.1016/S0024-3795(97)80052-3

[5]

Karpelevic FI., 1951, IZV AKAD NAUK SSSR M, V15, P361

[6]

Perfect H., 1965, Monatsh. Math, V69, P35

[7] Research on Markoff chains - First paper [J].

Romanovsky, V .

ACTA MATHEMATICA, 1936, 66 (01) :147-251

[8]

ROMANOVSKY VI, DISCRETE MARKOV CHAI

[9]

Swift J., 1972, THESIS MCGILL U

← 1 →