The Re-nonnegative definite and Re-positive definite solutions to the matrix equation AXBÂ =Â D

In this paper the Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions of the matrix equation AXB = D are considered. The necessary and sufficient conditions for the existence of Re-nnd and Re-pd solutions to the equation are provided and the explicit representations of the general Re-nnd and Re-pd solutions are given when it is solvable.