首页|Stochastic matrices realising the boundary of the Karpelevic region
Stochastic matrices realising the boundary of the Karpelevic region
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NSTL
Elsevier
A celebrated result of Karpelevic describes circle minus(n), the collection of all eigenvalues arising from the stochastic matrices of order n. The boundary of circle minus(n) consists of roots of certain one-parameter families of polynomials, and those polynomials are naturally associated with the so-called reduced Ito polynomials of Types 0, I, II and III. In this paper we explicitly characterise all n x n stochastic matrices whose characteristic polynomials are of Type 0 or Type I, and all sparsest stochastic matrices of order n whose characteristic polynomials are of Type II or Type III. The results provide insights into the structure of stochastic matrices having extreme eigenvalues. (c) 2021 Elsevier Inc. All rights reserved.
Stochastic matrixEigenvalueMarkov chainKarpelevic region
NSTL
Elsevier
