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A Class of Quadratic Matrix Equations over Finite Fields

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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 gen-erating set for the vanishing ideal of these orbits.

matrix equationsgeneral linear groupsfinite fieldsseparating invariants

Yin Chen、Xinxin Zhang

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School of Mathematics and Statistics,Northeast Normal University Changchun 130024,China

Department of Mathematics and Statistics,Queen's University Kingston,K7L 3N6,Canada

NNSF of China

11401087

2023

10.1142/S1005386723000147

代数集刊(英文版)

代数集刊(英文版)

CSCD北大核心
ISSN：1005-3867
年,卷(期)：2023.30(1)
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