K-Primitivity : A Literature Survey
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914695930183680 |
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| author | Nej, Monimala |
| author_facet | Nej, Monimala |
| contents | A nonnegative matrix A is said to be primitive if there exists a positive integer m such that entries in A^m are positive and smallest such m is called the exponent of A: Primitive matrices are useful in the study of finite Markov chains theory. In 1998, in the context of finite Markov chains, Ettore Fornasini and Maria Elena Valcher [6] extended the notion of primitivity for a nonnegative matrix pair (A;B) by considering a positive discrete homogeneous two-dimensional (2D) state model. Further generalization to this notion of primitivity for k-tuple (A1;A2;...;Ak) of nonnegative matrices A1;A2;...;Ak is quite natural and known as k-primitivity. In this paper we present various results on k-primitivity given by different researchers from time to time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-Primitivity : A Literature Survey Nej, Monimala History and Overview Combinatorics AMS(2020): 05C50, 05C38, 15B99 A nonnegative matrix A is said to be primitive if there exists a positive integer m such that entries in A^m are positive and smallest such m is called the exponent of A: Primitive matrices are useful in the study of finite Markov chains theory. In 1998, in the context of finite Markov chains, Ettore Fornasini and Maria Elena Valcher [6] extended the notion of primitivity for a nonnegative matrix pair (A;B) by considering a positive discrete homogeneous two-dimensional (2D) state model. Further generalization to this notion of primitivity for k-tuple (A1;A2;...;Ak) of nonnegative matrices A1;A2;...;Ak is quite natural and known as k-primitivity. In this paper we present various results on k-primitivity given by different researchers from time to time. |
| title | K-Primitivity : A Literature Survey |
| topic | History and Overview Combinatorics AMS(2020): 05C50, 05C38, 15B99 |
| url | https://arxiv.org/abs/2402.18586 |