In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the η-anti-Hermitian solution to a system of constrained matrix equations over the generalized Segre quaternion algebra. We also obtain the expression of the general η-anti-Hermitian solution to the system when it is solvable. Finally, we provide a numerical example to verify the main results of this paper.
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