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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2008.12457 |
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| _version_ | 1866911785823502336 |
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| author | Chen, Yin Zhang, Xinxin |
| author_facet | Chen, Yin Zhang, Xinxin |
| contents | We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can be separated by classical conjugation invariants defined by characteristic polynomials. We also find a generating set for the vanishing ideal of these orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_12457 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A class of quadratic matrix equations over finite fields Chen, Yin Zhang, Xinxin Rings and Algebras 15A24, 15A35, 13A50 We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can be separated by classical conjugation invariants defined by characteristic polynomials. We also find a generating set for the vanishing ideal of these orbits. |
| title | A class of quadratic matrix equations over finite fields |
| topic | Rings and Algebras 15A24, 15A35, 13A50 |
| url | https://arxiv.org/abs/2008.12457 |