The four-dimensional Perfect-Mirsky Conjecture-Reference-Cited by-同舟云学术

The four-dimensional Perfect-Mirsky Conjecture

Published:2014-12-15 Issue:5 Volume:143 Page:1951-1956
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Levick Jeremy,Pereira Rajesh,Kribs David

Abstract

We verify the Perfect-Mirsky Conjecture on the structure of the set of eigenvalues for all n × n n \times n doubly stochastic matrices in the four-dimensional case. The n = 1 , 2 , 3 n=1,2,3 cases have been established previously and the n = 5 n=5 case has been shown to be false. Our proof is direct and uses basic tools from matrix theory and functional analysis. Based on this analysis we formulate new conjectures for the general case.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2015-143-05/S0002-9939-2014-12412-9/S0002-9939-2014-12412-9.pdf

Reference9 articles.

1. Eigenvalue regions for positive systems;Benvenuti, Luca;Systems Control Lett.,2004

2. Three observations on linear algebra;Birkhoff, Garrett;Univ. Nac. Tucum\'{a}n. Revista A.,1946

3. On characteristic roots of stochastic matrices;Dmitriev, N.;Bull. Acad. Sci. URSS. S\'{e}r. Math. [Izvestia Akad. Nauk SSSR],1946

4. An inclusion region for the field of values of a doubly stochastic matrix based on its graph;Johnson, Charles R.;Aequationes Math.,1978

5. Row stochastic matrices similar to doubly stochastic matrices;Johnson, Charles R.;Linear and Multilinear Algebra,1981

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. New views of the doubly stochastic single eigenvalue problem;Linear and Multilinear Algebra;2022-05-14

2. Conjectures about determining the regions of eigenvalues of stochastic and doubly stochastic matrices;Linear Algebra and its Applications;2022-03

3. Doubly stochastic matrices and the quantum channels;Journal of Applied Mathematics, Statistics and Informatics;2021-05-01

4. Spectra of convex hulls of matrix groups;Linear Algebra and its Applications;2020-05

5. The Doubly Stochastic Single Eigenvalue Problem: A Computational Approach;Experimental Mathematics;2020-03-10