  In this article we apply proper splittings of matrices to develop an
iterative process to approximate solutions of matrix equations of the form TX =
W. Moreover, by using the partial order induced by positive semidefinite
matrices, we obtain equivalent conditions to the convergence of this process.
We also include some speed comparison results of the convergence of this
method. In addition, for all matrix T we propose a proper splitting based on
the polar decomposition of T.
