Stochastic matrices and majorization in max algebra
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909595789688832 |
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| author | Manjegani, S. M. Parsa, T. |
| author_facet | Manjegani, S. M. Parsa, T. |
| contents | In this paper, we introduce and characterize max-doubly stochastic matrices within the framework of max algebra, where the operations are defined as $x \oplus y = \max(x, y)$ and $x \otimes y = xy$. We explore the fundamental properties of max-doubly stochastic matrices and their role in vector majorization. Specifically, we establish that for vectors $x$ and $y$ in max algebra, $x$ is majorized by $y$ if there exists a max-doubly stochastic matrix $D$ such that $x = D \otimes y$. This provides a new approach to majorization theory within tropical mathematics and enhances the understanding of vector relations in max algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19340 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic matrices and majorization in max algebra Manjegani, S. M. Parsa, T. Rings and Algebras 15A80, 15B51, 06A06 In this paper, we introduce and characterize max-doubly stochastic matrices within the framework of max algebra, where the operations are defined as $x \oplus y = \max(x, y)$ and $x \otimes y = xy$. We explore the fundamental properties of max-doubly stochastic matrices and their role in vector majorization. Specifically, we establish that for vectors $x$ and $y$ in max algebra, $x$ is majorized by $y$ if there exists a max-doubly stochastic matrix $D$ such that $x = D \otimes y$. This provides a new approach to majorization theory within tropical mathematics and enhances the understanding of vector relations in max algebra. |
| title | Stochastic matrices and majorization in max algebra |
| topic | Rings and Algebras 15A80, 15B51, 06A06 |
| url | https://arxiv.org/abs/2504.19340 |