Some Rank Formulas for the Yang-Baxter Matrix Equation AXA=XAX  

作　　者：DAI Lifang LIANG Maolin SHEN Yonghong 

机构地区：[1]School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,Gansu,China

出　　处：《Wuhan University Journal of Natural Sciences》2021年第6期459-463,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China(11961057);the Science and Technology Project of Gansu Province(21JR1RE287 and 2021B-221);the Fuxi Scientific Research Innovation Team of Tianshui Normal University(FXD2020-03);the Science Foundation(CXT2019-36 and CXJ2020-11);the Education and Teaching Reform Project of Tianshui Normal University(JY202004 and JY203008)。

摘　　要：Let A be an arbitrary square matrix,then equation AXA=XAX with unknown X is called Yang-Baxter matrix equation.It is difficult to find all the solutions of this equation for any given A.In this paper,the relations between the matrices A and B are established via solving the associated rank optimization problem,where B=AXA=XAX,and some analytical formulas are derived,which may be useful for finding all the solutions and analyzing the structures of the solutions of the above Yang-Baxter matrix equation.

关 键 词：Yang-Baxter matrix equation RANK generalized inverse 

分 类 号：O124.6[理学—数学]