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Conjectures about determining the regions of eigenvalues of stochastic and doubly stochastic matrices
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NSTL
Elsevier
Let the regions circle minus(n) and omega(n) be the subsets of the complex planes that consist of all eigenvalues of all n x n stochastic and doubly stochastic matrices, respectively. Also, let Pi(n) denote the convex hull of the nth roots of unity. Levick, Pereira and Kribs (2015) [10] made the following conjectures on the relations between circle minus(n), omega(n) and Pi(n): omega(n) = circle minus(n-1) boolean OR Pi(n) and circle minus(n-1) subset of omega(n). These two conjectures are known to be true for n = 2, 3, 4. In this paper, we will show that these two conjectures are not true for n >= 5. (c) 2021 Elsevier Inc. All rights reserved.
NSTL
Elsevier
