On the trace-zero doubly stochastic matrices of order 5
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913555000852480 |
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| author | Mandal, Amrita Adhikari, Bibhas |
| author_facet | Mandal, Amrita Adhikari, Bibhas |
| contents | We propose a graph theoretic approach to determine trace of product of two permutation matrices through a weighted digraph representation of the permutation matrices. Consequently, we derive trace-zero doubly stochastic (DS) matrices of order $5$ whose $k$-th power is also a trace-zero DS matrix for $k\in\{2,3,4,5\}$. Then, we determine necessary conditions for the coefficients of a generic polynomial of degree $5$ to be realizable as the characteristic polynomial of a trace-zero DS matrix of order $5$. Finally, we approximate the eigenvalue region of trace-zero DS matrices of order $5.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06810 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the trace-zero doubly stochastic matrices of order 5 Mandal, Amrita Adhikari, Bibhas Combinatorics Spectral Theory We propose a graph theoretic approach to determine trace of product of two permutation matrices through a weighted digraph representation of the permutation matrices. Consequently, we derive trace-zero doubly stochastic (DS) matrices of order $5$ whose $k$-th power is also a trace-zero DS matrix for $k\in\{2,3,4,5\}$. Then, we determine necessary conditions for the coefficients of a generic polynomial of degree $5$ to be realizable as the characteristic polynomial of a trace-zero DS matrix of order $5$. Finally, we approximate the eigenvalue region of trace-zero DS matrices of order $5.$ |
| title | On the trace-zero doubly stochastic matrices of order 5 |
| topic | Combinatorics Spectral Theory |
| url | https://arxiv.org/abs/2311.06810 |