We determine some necessary and sufficient conditions for the existence of the η-skew-Hermitian solution to the following system AX-(AX)η⁎+BYBη⁎+CZCη⁎=D,Y=-Yη⁎,Z=-Zη⁎ over the quaternion skew field and provide an explicit expression of… Click to show full abstract
We determine some necessary and sufficient conditions for the existence of the η-skew-Hermitian solution to the following system AX-(AX)η⁎+BYBη⁎+CZCη⁎=D,Y=-Yη⁎,Z=-Zη⁎ 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.
Journal Title: Mathematical Problems in Engineering
Year Published: 2019
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