论文标题
有限字段的一类二次矩阵方程
A class of quadratic matrix equations over finite fields
论文作者
论文摘要
我们为有限场上的一类二次矩阵方程的解决方案的基数表现出明确的公式。我们证明，在通用线性组的自然共轭作用下，这些溶液的轨道可以通过特征多项式定义的经典共轭不变性分离。我们还发现了这些轨道消失理想的生成集。
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.
