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.
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 language | English |
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Title of host publication | Proceedings Nonnegative Matrices and Finite Markov Chains 2024 |
Publisher | Waset |
Pages | 26-26 |
Number of pages | 1 |
ISBN (Electronic) | 1307-6892 |
Publication status | Published - 2024 |
Event | International conference on nonnegative matrices and finite Markov chains - Venice, Italy Duration: 20 Jun 2024 → 21 Jun 2024 https://waset.org/nonnegative-matrices-and-finite-markov-chains-conference-in-june-2024-in-venice |
Conference
Conference | International conference on nonnegative matrices and finite Markov chains |
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Abbreviated title | ICNMFMC 2024 |
Country/Territory | Italy |
City | Venice |
Period | 20/06/24 → 21/06/24 |
Internet address |
Keywords
- Eigenvalues of matrices
- Finite Markov chains
- Monotone matrices
- Nonnegative matrices
- Stochastic matrices