Explicit determinantal representation formulas for the solution of the two-sided restricted quaternionic matrix equation

Abstract

Weighted singular value decomposition 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 quaternionic 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.