Based on the properties of the core-EP inverse and its dual, we investigate three variants of a novel quaternion-matrix (Q-matrix) approximation problem in the Frobenius norm: \(\min \Vert \mathbf {A}\mathbf {X}\mathbf {B}-\mathbf {C}\Vert _F\) subject to the constraints imposed to the right column space of \({\mathbf{A}}\) and the left row space of \({\mathbf{B}}\). Unique solution to the considered Q-matrix problem is expressed in terms of the core inverse of \({\mathbf{A}}\) and/or the dual core-EP inverse of \({\mathbf{B}}\). Thus, we propose and solve problems which generalize a well-known constrained approximation problem for complex matrices with index one to quaternion matrices with arbitrary index. Determinantal representations for solutions of proposed constrained quaternion matrix approximation problems obtained. An example is given to justify obtained theoretical results.

基于核心EP逆及其对偶的性质，我们研究了Frobenius范数中一个新的四元数矩阵（Q矩阵）逼近问题的三个变体：\（\ min \ Vert \ mathbf {A} \ mathbf { X} \ mathbf {B}-\ mathbf {C} \ Vert _F \）受制于对\（{\ mathbf {A}} \）的右列空间和\（{\ mathbf {B}} \）。对所考虑的Q矩阵问题的唯一解可用\（{\ mathbf {A}} \）的核心逆和/或\（{\ mathbf {B}} \}的双核EP来表达。因此，我们提出并解决了一些问题，这些问题将索引为1的复数矩阵推广为任意索引的四元数矩阵的一般约束逼近问题。确定性四元数矩阵逼近问题解的行列式表示。举例说明了所获得的理论结果。