Compact formula for skew-symmetric system of matrix equations

In this paper, we consider skew-Hermitian solution of coupled generalized Sylvester matrix equations encompassing ∗-hermicity over complex field. The compact formula of the general solution of this system is presented in terms of generalized inverses when some necessary and sufficient conditions are fulfilled. An algorithm and a numerical example are provided to validate our findings. A numerical example is carried out using determinantal representations of the Moore–Penrose inverse.