Tropical Matrix Exponential
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929440210026496 |
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| author | M, Askar Ali Mukherjee, Himadri |
| author_facet | M, Askar Ali Mukherjee, Himadri |
| contents | In this article, we introduce an exponential for tropical matrices and show that this series is essential for the analysis of certain kinds of stability in discrete event dynamic systems. A notion of a generalised eigenvector is introduced to discuss this kind of stability and prove it exists at most in the order of $1,p/2,p$, where $p$ is the period of the corresponding matrix. Thus characterizing the generalised eigenvectors of all powers of the matrix. Also, a sufficient condition is proved for the exponential of a matrix to be robust. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropical Matrix Exponential M, Askar Ali Mukherjee, Himadri Rings and Algebras 15A80, 15A16 In this article, we introduce an exponential for tropical matrices and show that this series is essential for the analysis of certain kinds of stability in discrete event dynamic systems. A notion of a generalised eigenvector is introduced to discuss this kind of stability and prove it exists at most in the order of $1,p/2,p$, where $p$ is the period of the corresponding matrix. Thus characterizing the generalised eigenvectors of all powers of the matrix. Also, a sufficient condition is proved for the exponential of a matrix to be robust. |
| title | Tropical Matrix Exponential |
| topic | Rings and Algebras 15A80, 15A16 |
| url | https://arxiv.org/abs/2407.19786 |