We first investigate some necessary and sufficient conditions for the solvability to a constraint system of coupled two-sided Sylvester-like quaternion tensor equations. We also construct an expression of the general solution to the system above when it is solvable. As an application of the system, we discuss some solvability conditions and the \(\eta \)-Hermitian solution to some system of Sylvester-like quaternion tensor equations.

中文翻译：

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耦合两边类Sylvester四元数张量方程的约束系统

我们首先研究一些必要条件和充分条件，以解决两边类Sylvester耦合四元数张量方程的约束系统。当可解时，我们还将构造上述系统的一般解的表达式。作为该系统的应用，我们讨论了一些类似于Sylvester四元数张量方程组的系统的可解性条件和\（\ eta \）- Hermitian解。