English

A class of quadratic matrix equations over finite fields

Rings and Algebras 2024-03-01 v3

Abstract

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.

Keywords

Cite

@article{arxiv.2008.12457,
  title  = {A class of quadratic matrix equations over finite fields},
  author = {Yin Chen and Xinxin Zhang},
  journal= {arXiv preprint arXiv:2008.12457},
  year   = {2024}
}

Comments

To appear in Algebra Colloquium

R2 v1 2026-06-23T18:09:25.508Z