In this paper, we use the equivalence canonical form of four quaternion matrices to consider two systems of quaternion matrix equations. We derive some practical necessary and sufficient conditions for the existence of a solution to these two systems in terms of ranks of the quaternion matrices involved. We also give the general solutions to the systems when the solvability conditions are satisfied. Moreover, we present some numerical examples to illustrate the results of this paper.

中文翻译：

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具有两个不同约束的四元数矩阵方程

在本文中，我们使用四个四元数矩阵的等价正则形式来考虑两个四元数矩阵方程组。我们根据所涉及的四元数矩阵的秩，得出了这两个系统的解的存在的一些实际必要和充分条件。当满足可溶性条件时，我们还提供了系统的一般解决方案。此外，我们提供一些数值示例来说明本文的结果。