Preservers of partial orders on the set of all variance-covariance matrices

Let H+n(R) be the cone of all positive semidefinite n x real matrices. Two best known partial orders that were mostly studied on subsets square complex matrices are L?wner and minus orders. Motivated by applications in statistics we study these H+ (R). We describe form surjective maps (R), > 1, preserve order both directions. present an equivalent definition (R) also characterize surjective, additive ? 3,