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arXiv · 1708.01515

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

Ivan Kyrchei
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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, ${\bf A}{\bf X}{\bf B}={\bf D}$, and consequently, ${\bf A}{\bf X}={\bf D}$ and ${\bf X}{\bf B}={\bf D}$ are obtained within the framework of the theory of column-row determinants. We consider all possible cases depending on weighted matrices.

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Ivan Kyrchei. 2017-08-02. Cramer's rules for the solution to the two-sided restricted quaternion matrix equation. https://arxiv.org/abs/1708.01515

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