Cramer's rule for some quaternion matrix equations

TL;DR

This paper develops Cramer's rule solutions for certain quaternion matrix equations using the theory of column and row determinants, expanding the methods available for solving quaternion linear systems.

Contribution

It introduces Cramer's rule formulations for specific quaternion matrix equations based on column and row determinant theory, which was not previously established.

Findings

Derived explicit Cramer's rule formulas for quaternion equations

Extended classical Cramer's rule to quaternion matrices

Provided theoretical framework for solving quaternion matrix equations

Abstract

Cramer's rules for some left, right and two-sided quaternion matrix equations are obtained within the framework of the theory of the column and row determinants.