The paper deals with extremal rank solutions to a system of quaternion matrix equations.
denotes the set of matrices over the real quaternion algebra
A matrix is called -symmetric (or -skewsymmetric) if (or ), where and are involution matrices. Consider the system of matrix equations over
In this work, the authors analyze the -(skew)symmetric maximal and minimal rank solutions of this system. They obtain necessary and sufficient conditions for the existence of -symmetric and -skewsymmetric solutions to the above system and give the expressions of such solutions when the solvability conditions are satisfied.
The authors also establish formulas of maximal and minimal ranks of -symmetric and -skewsymmetric solutions of (*) and derive the expressions of -(skew)symmetric maximal and minimal rank solutions of (*).
Finally, the authors present a numerical example that confirms the theoretical results obtained.