Date Thesis Awarded
Honors Thesis -- Open Access
Bachelors of Science (BS)
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.
Wilkes, John and Johnson, Charles Royal, "The Doubly Stochastic Single Eigenvalue Problem: An Empirical Approach" (2018). Undergraduate Honors Theses. Paper 1258.
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