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The Doubly Stochastic Single Eigenvalue Problem: An Empirical Approach
Wilkes, John Johnson, Charles Royal
Wilkes, John
Johnson, Charles Royal
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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2018-05-01
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Mathematics