Open AccessThe four-dimensional Perfect-Mirsky Conjecture
Author(s) -
Jeremy Levick,
Rajesh Pereira,
David W. Kribs
Publication year - 2014
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-2014-12412-9
Subject(s) - algorithm , computer science , annotation , artificial intelligence
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.