Generalized Sylvester quaternion matrix equation with some constrictions is explored in this paper. A novel expression of the general solution of the constraint system is given with some necessary and sufficient conditions. Its Cramer’s rule is derived within the framework of the theory of row-column quaternion determinants. An example is given to justify obtained theoretical results.

中文翻译：

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经典四元数矩阵方程组的约束解及其克雷姆规则

本文探讨了具有某些约束条件的广义Sylvester四元数矩阵方程。给出了约束系统一般解的新颖表达，并给出了一些必要和充分的条件。它的克拉默法则是在行列四元数行列式理论的框架内得出的。举例说明了所获得的理论结果。