linear preservers of g-matrices on m2 ‎

Let mn be the set of all n×n real matrices. a nonsingular matrix a ∈ mn is called a g-matrix if there exist nonsingular diagonal matrices d1 and d2 such that a−t= d1ad2, where a−t denotes the transpose of the inverse of a. let gn be the set of all n×n g-matrices. a linear operator t : mn → mn is called a linear preserver of g-matrices if t(gn) ⊆ gn. the purpose of this paper is to find the structure of the linear operator preserving g-matrices on m2.