The General Solution of Quaternion Matrix Equation Having η -Skew-Hermicity and Its Cramer’s Rule

Abstract EN

We determine some necessary and sufficient conditions for the existence of the η -skew-Hermitian solution to the following system A X - ( A X ) η ⁎ + B Y B η ⁎ + C Z C η ⁎ = D , Y = - Y η ⁎ , Z = - Z η ⁎ over the quaternion skew field and provide an explicit expression of its general solution.

Within the framework of the theory of quaternion row-column noncommutative determinants, we derive its explicit determinantal representation formulas that are an analog of Cramer’s rule.

A numerical example is also provided to establish the main result.