On the Solutions of Some Linear Complex Quaternionic Equations

الملخص EN

Some complex quaternionic equations in the type AX-XB=C are investigated.

For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases.

By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.