  Many applications in applied mathematics and control theory give rise to the
unique solution of a Sylvester-like matrix equation associated with an
underlying structured matrix operator $f$. In this paper, we will discuss the
solvability of the Sylvester-like matrix equation through an auxiliary standard
(or generalized) Sylvester matrix equation. We also show that when this
Sylvester-like matrix equation is uniquely solvable, the closed-form solutions
can be found by using previous result. In addition, with the aid of the
Kronecker product some useful results of the solvability of this matrix
equation are provided.
