We consider the solvability of four new restricted quaternion matrix equations (QME) and prove that these equations have the unique solutions determined by adequate MPD and DMP inverses. Several particular cases of these equations are presented too. Determinantal representations of solutions to new constrained equations and their particular cases are developed. An illustrative numerical example is given to illustrate gained results.

中文翻译：

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四元数两侧受限矩阵方程的 MPD-DMP 解

我们考虑了四个新的受限四元数矩阵方程 (QME) 的可解性，并证明这些方程具有由足够的 MPD 和 DMP 逆确定的唯一解。还介绍了这些方程的几个特殊情况。开发了新约束方程及其特殊情况的解的行列式表示。给出了一个说明性的数值例子来说明获得的结果。