Cramer's rules for Hermitian systems of coquaternionic equations

TL;DR

This paper investigates determinants of Hermitian coquaternionic matrices, providing determinantal formulas for their inverses and deriving Cramer's rules for solving related linear systems, including two-sided matrix equations.

Contribution

It introduces new determinantal representations and Cramer's rules specifically for Hermitian coquaternionic matrices, extending classical linear algebra results to this non-commutative setting.

Findings

Determinantal representations of Hermitian coquaternionic matrix inverses

Cramer's rules for systems with Hermitian coquaternionic coefficient matrices

Solution formulas for two-sided coquaternionic matrix equations

Abstract

In this paper properties of the determinant of a Hermitian matrix are investigated, and determinantal representations of the inverse of a Hermitian coquaternionic matrix are given. By their using, Cramer's rules for left and right systems of linear equations with Hermitian coquaternionic matrices of coefficients are obtained. Cramer's rule for a two-sided coquaternionic matrix equation ${\bf AXB}={\bf D}$ (with Hermitian ${\bf A}$, ${\bf B}$) is given as well.