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 t...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11971294).
文摘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.
