Date Thesis Awarded

5-2018

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Charles Johnson

Committee Members

Eric Swartz

Andreas Stathopoulos

Abstract

The doubly stochastic single eigenvalue problem asks what is the set DS_n of all complex numbers that occur as an eigenvalue of an n-by-n doubly stochastic matrix. For n < 5, this set is known and for the analogous set for (singly) stochastic matrices, the set is known for all n. For P_k , the polygon formed by the k-th roots of unity, Uⁿ_k=1 P_k ⊆ DS_n, as is easily shown. For n < 5, this containment is an equality, but for n = 5, the containment is strict (though it is close). Presented here is substantial, computational evidence that the containment is an equality for 6 ≤ n ≤ 10 and for what DS₅ actually is.

Recommended Citation

Wilkes, John and Johnson, Charles Royal, "The Doubly Stochastic Single Eigenvalue Problem: An Empirical Approach" (2018). Undergraduate Honors Theses. William & Mary. Paper 1258.
https://scholarworks.wm.edu/honorstheses/1258