Solutions to the nonhomogeneous generalized Sylvester quaternion j-conjugate matrix equation

In this article, we develop a real representation method for computing the solution pair (X, Y) to the non-homogeneous generalized Sylvester quaternion j-conjugate matrix equation XB - AX̑ = CY + R. Compared to the existing complex representation method [C. Song, G. Chen, Acta Mathematica Scientia 2012, 32(B)(5):1967-1982], the advantage of this new approach is that there is no special requirement on the any coefficient matrix. In this sense, we generalize the existing results. Finally, a numerical example is provided to support the theoretical findings and to testify the effectiveness and usefulness of the developed algorithm.