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The solvability and the exact solution of a system of real quaternion matrix equations. (English) Zbl 1263.15016

Authors’ abstract: We establish necessary and sufficient conditions for the solvability of the system of real quaternion matrix equations \[ \begin{cases} {A}_{1}X=C_{1},~ \\ YB_{1}=D_{1}, \\ A_{2}Z=C_{2},ZB_{2}=D_{2},A_{3}ZB_{3}=C_{3}, \\ A_{4}X+YB_{4}+C_{4}ZD_{4}=E_{1}.\end{cases} \] We also present an expression of the general solution to the system. The findings of this paper widely extend the known results in the literature.

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A09 Theory of matrix inversion and generalized inverses
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