A Class of Quadratic Matrix Equations over Finite Fields  

作　　者：Yin Chen Xinxin Zhang 

机构地区：[1]School of Mathematics and Statistics,Northeast Normal University Changchun 130024,China [2]Department of Mathematics and Statistics,Queen's University Kingston,K7L3N6,Canada

出　　处：《Algebra Colloquium》2023年第1期169-180,共12页代数集刊（英文版）

基　　金：supported by the NNSF of China(Grant No.11401087).

摘　　要：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.

关 键 词：matrix equations general linear groups finite fields separating invariants 

分 类 号：O17[理学—数学]