Reducible solution to a quaternion tensor equation  

作　　者：Mengyan XIE Qing-Wen WANG 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Frontiers of Mathematics in China》2020年第5期1047-1070,共24页中国高等学校学术文摘·数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11971294).

摘　　要：We establish necessary and sufficient conditions for the existence of the reducible solution to the quaternion tensor equation A*N C*NB=C via Einstein product using Moore-Penrose inverse,and present an expression of the reducible solution to the equation when it is solvable.Moreover,to have a general solution,we give the solvability conditions for the quaternion tensor equation A1*N C1*MB1+a1*C2*MB2+A2*NC3*MB2=e,which plays a key role in investigating the reducible solution to A*NC*NB=e.The expression of such a solution is also presented when the consistency conditions are met.In addition,we show a numerical example to illustrate this result.

关 键 词：Quaternion tensor quaternion tensor equation Einstein product Moore-Penrose inverse general solution reducible solution 

分 类 号：O17[理学—数学]