A system of quaternary coupled Sylvester-type real quaternion matrix equations

In this paper we establish some necessary and sufficient solvability conditions for a system of quaternary coupled Sylvester-type real quaternion matrix equations in terms of ranks and generalized inverses of matrices. An expression of the general solution to this system is given when it is solvable. Also, a numerical example is presented to illustrate the main result of this paper. The findings of this paper widely generalize the known results in the literature. The main results are also valid over the real number field and the complex number field.