Cramer's rules for the solution to the two-sided restricted quaternion matrix equation

Abstract

Weighted singular value decomposition (WSVD) of a quaternion matrix and with its help determinantal representations of the quaternion weighted Moore-Penrose inverse have been derived recently by the author. In this paper, using these determinantal representations, explicit determinantal representation formulas for the solution of the restricted quaternion matrix equations, $\mathbf{A}\mathbf{X}\mathbf{B}=\mathbf{D}$, and consequently, $\mathbf{A}\mathbf{X}=\mathbf{D}$ and $\mathbf{X}\mathbf{B}=\mathbf{D}$ are obtained within the framework of the theory of column-row determinants. We consider all possible cases depending on weighted matrices.

arXiv admin note: text overlap with arXiv:1604.00243