A new technique for solving continuous Sylvester-conjugate matrix equation AX − X̅B = C

In this paper, the explicit solutions to the matrix equation AX - X̅B = C have been given by using of the so-called Leverrier algorithm. While one of the explicit solutions is stated as a polynomial of coefficient matrices of the matrix equation. Comparing to the existing results, there is no requirement on the coefficient matrices. Furthermore, a numerical example is presented to show the effectiveness of the proposed method.