Stochastic matrices realising the boundary of the Karpelevič region
| Autor: | Stephen J. Kirkland, Helena Šmigoc |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Numerical Analysis
Pure mathematics Algebra and Number Theory 0211 other engineering and technologies Structure (category theory) Boundary (topology) 021107 urban & regional planning 02 engineering and technology 010501 environmental sciences Type (model theory) 01 natural sciences Discrete Mathematics and Combinatorics Order (group theory) Geometry and Topology Eigenvalues and eigenvectors 0105 earth and related environmental sciences Mathematics |
| Zdroj: | Linear Algebra and its Applications. 635:116-138 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2021.11.016 |
| Popis: | A celebrated result of Karpelevic describes Θ n , the collection of all eigenvalues arising from the stochastic matrices of order n. The boundary of Θ 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 × 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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