A Class of Quadratic Matrix Equations over Finite Fields

被引：0

作者：

Chen, Yin ^{[1
,2
]}

Zhang, Xinxin ^{[1
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

来源：

ALGEBRA COLLOQUIUM | 2023年 / 30卷 / 01期

关键词：

matrix equations; general linear groups; finite fields; separating invariants; INVARIANTS;

D O I：

10.1142/S1005386723000147

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：169 / 180

页数：12

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