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Let H m×n be the set of all m × n matrices over the real quaternion algebra.We in this paper, present the solvability conditions and the general η-Hermitian solution to a system of linear real quaternion matrix equations. As an application, we give the necessary and sufficient conditions for the systemWe establish an expression of the η-bihermitian to the system when it is solvable. We also obtain a criterion for a quaternion matrix to be η-bihermitian. Moreover, we provide an algorithm and a numerical example to illustrate the theory developed in this paper.

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