A System of Coupled Two-sided Sylvester-type Tensor Equations over the Quaternion Algebra

Abstract

We establish some necessary and sufficient conditions for the solvability to a system of a pair of coupled two-sided Sylvester-type tensor equations over the quaternion algebra. We also give an expression of the general solution to the system when it is solvable. As applications, we derive some solvability conditions and expressions of the $\eta$-Hermitian solutions to some systems of coupled two-sided Sylvester-type quaternion tensor equations. Moreover, we provide an example to illustrate the main results of this paper.