On affine homogeneous polynomial centrosymmetric matrices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912294637666304 |
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| author | Manoel, Miriam Nery, Leandro |
| author_facet | Manoel, Miriam Nery, Leandro |
| contents | We explore a class of centrosymmetric matrices whose entries are polynomials in two variables, referred to as DNA matrices. Our motivation stems from an unexpected connection between these matrices and invariant polynomials under the action of a Lorentz rotation on the plane. Among several noteworthy properties, we establish that within a subclass of DNA matrices, singular matrices occur precisely when their order is even, and we determine their null space in such cases. The results provide new insights into the structural characteristics of centrosymmetric matrices, expanding their theoretical foundations and potential applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20141 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On affine homogeneous polynomial centrosymmetric matrices Manoel, Miriam Nery, Leandro Rings and Algebras 13A50, 15A24, 20C32, 20G05, 22E43, 22E70 We explore a class of centrosymmetric matrices whose entries are polynomials in two variables, referred to as DNA matrices. Our motivation stems from an unexpected connection between these matrices and invariant polynomials under the action of a Lorentz rotation on the plane. Among several noteworthy properties, we establish that within a subclass of DNA matrices, singular matrices occur precisely when their order is even, and we determine their null space in such cases. The results provide new insights into the structural characteristics of centrosymmetric matrices, expanding their theoretical foundations and potential applications. |
| title | On affine homogeneous polynomial centrosymmetric matrices |
| topic | Rings and Algebras 13A50, 15A24, 20C32, 20G05, 22E43, 22E70 |
| url | https://arxiv.org/abs/2503.20141 |