Geometric and Algebraic Properties of the Eigenvalues of Monotone Matrices

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Abstract

For stochastic matrices of any order the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrices appears in contexts such as intergenerational occupational mobility, equal-input modeling and credit ratings based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1).

Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight in the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.
Original languageEnglish
Title of host publicationProceedings Nonnegative Matrices and Finite Markov Chains 2024
PublisherWaset
Pages26-26
Number of pages1
ISBN (Electronic)1307-6892
Publication statusPublished - 2024
EventInternational conference on nonnegative matrices and finite Markov chains - Venice, Italy
Duration: 20 Jun 202421 Jun 2024
https://waset.org/nonnegative-matrices-and-finite-markov-chains-conference-in-june-2024-in-venice

Conference

ConferenceInternational conference on nonnegative matrices and finite Markov chains
Abbreviated title ICNMFMC 2024
Country/TerritoryItaly
CityVenice
Period20/06/2421/06/24
Internet address

Keywords

  • Eigenvalues of matrices
  • Finite Markov chains
  • Monotone matrices
  • Nonnegative matrices
  • Stochastic matrices

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