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The general solution to a system of real quaternion matrix equations. (English) Zbl 1138.15004

Summary: We consider the system of matrix equations, \(A_{1}X = C_{1}, A_{2}X = C_{2}\), \(A_{3}XB_{3} = C_{3}\), and \(A_{4}XB_{4} = C_{4}\), over the real quaternion algebra \(\mathbb H\) . Necessary and sufficient conditions for the existence and the expression of the general solution to the system are given. As particular cases, the corresponding results on other systems over \(\mathbb H\) are also obtained.

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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