The Karpelevič region revisited
| Autor: | Stephen J. Kirkland, Helena Šmigoc, Thomas J. Laffey |
|---|---|
| Přispěvatelé: | University of Manitoba |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Functional Analysis
Markov chain Applied Mathematics 010102 general mathematics Stochastic matrix stochastic matrix Boundary (topology) 01 natural sciences 010101 applied mathematics Combinatorics Mathematics::Category Theory eigenvalue Order (group theory) 0101 mathematics Analysis Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 490:124332 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2020.124332 |
| Popis: | We consider the Karpelevic region Θ n ⊂ C consisting of all eigenvalues of all stochastic matrices of order n. We provide an alternative characterisation of Θ n that sharpens the original description given by Karpelevic. In particular, for each θ ∈ [ 0 , 2 π ) , we identify the point on the boundary of Θ n with argument θ. We further prove that if n ∈ N with n ≥ 2 , and t ∈ Θ n , then t is a subdominant eigenvalue of some stochastic matrix of order n. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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