Matrix equivalence to Smith normal form: new theoretical results for multivariate polynomial matrices
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910205885808640 |
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| author | Lu, Dong Ruan, Yuanyuan Wang, Dingkang Xiao, Fanghui |
| author_facet | Lu, Dong Ruan, Yuanyuan Wang, Dingkang Xiao, Fanghui |
| contents | This paper investigates the Smith normal form equivalence problem for multivariate polynomial matrices. Using methods from matrix theory and polynomial ideal theory, we prove that Frost and Storey's 1978 conjecture holds for a broad class of matrices: such a matrix is equivalent to its Smith normal form if and only if its reduced minors of each order generate the unit ideal. Moreover, by extending the original matrix class via automorphisms of the polynomial ring, we show that our framework applies in a substantially more general setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09286 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matrix equivalence to Smith normal form: new theoretical results for multivariate polynomial matrices Lu, Dong Ruan, Yuanyuan Wang, Dingkang Xiao, Fanghui Commutative Algebra Symbolic Computation 15A24, 68W30 This paper investigates the Smith normal form equivalence problem for multivariate polynomial matrices. Using methods from matrix theory and polynomial ideal theory, we prove that Frost and Storey's 1978 conjecture holds for a broad class of matrices: such a matrix is equivalent to its Smith normal form if and only if its reduced minors of each order generate the unit ideal. Moreover, by extending the original matrix class via automorphisms of the polynomial ring, we show that our framework applies in a substantially more general setting. |
| title | Matrix equivalence to Smith normal form: new theoretical results for multivariate polynomial matrices |
| topic | Commutative Algebra Symbolic Computation 15A24, 68W30 |
| url | https://arxiv.org/abs/2605.09286 |