Cramer's rules for Hermitian systems of coquaternionic 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 $\mathbf{AXB}=\mathbf{D}$ (with Hermitian $\mathbf{A}$, $\mathbf{B}$) is given as well.

arXiv admin note: text overlap with arXiv:math/0702447

References in corpus (2)

• Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations
• The column and row immanants of matrices over a split quaternion algebra