幂零矩阵下二次矩阵方程AXA=XAX的反交换解  

On the Anticommuting Solutions of a Quadratic Matrix Equation for Nilpotent Matrix

作　　者：叶祥兴 蒋明谕 刘佳 韩蕊 陈小燕 YE Xiangxing;JIANG Mingyu;LIU Jia;HAN Rui;CHEN Xiaoyan(School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341000,China;Library,Gannan Normal University,Ganzhou 341000,China;Ruichang No.2 Middle School,Ruichang 332200,China)

机构地区：[1]赣南师范大学数学与计算机科学学院,江西赣州341000 [2]赣南师范大学赣南师范大学图书馆,江西赣州341000 [3]瑞昌市第二中学,江西瑞昌332200

出　　处：《赣南师范大学学报》2022年第6期12-18,共7页Journal of Gannan Normal University

基　　金：赣南师范大学研究基金(18zb04);大学生创新训练计划项目(CX200025)。

摘　　要：令A是一个任意的幂零矩阵,并考虑Yang-Baxter-like矩阵方程AXA=XAX.首先通过相似变换用矩阵A的Jordan标准型得到同型的更简洁的方程.然后找到原矩阵方程所有反交换解的结构.最后给出了2个例子来说明文章的理论结果.Let A be an arbitrary nilpotent matrix and consider the Yang-Baxter-like matrix equation AXA=XAX. We first obtain a simplified matrix equation of the same type with A replaced by its Jordan form. Then we obtain the structure of all the anticommuting solutions of the original matrix equation. Explicit examples are provided after almost every theoretical result. Finally, we give two examples to illustrate our theoretical results.

关 键 词：二次矩阵方程 幂零矩阵 JORDAN标准型 反交换解 

分 类 号：O241.6[理学—计算数学]