Date Thesis Awarded

5-2018

Document Type

Dissertation/Thesis

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 DSn 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 Pk , the polygon formed by the k-th roots of unity, Unk=1 Pk ⊆ DSn, 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.

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Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

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