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.
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)。
