Linear preservers of G-matrices on M۲

Let Mn be the set of all n × n real matrices. A nonsingular matrix A ∈ Mn iscalled a G-matrix if there exist nonsingular diagonal matrices D۱ and D۲ such thatA−T = D۱AD۲, where A−T denotes the transpose of the inverse of A. Let Gn be theset of all n×n G-matrices. A linear operator T : Mn → Mn is called a linear preserverof G-matrices if T(Gn) ⊆ Gn. The purpose of this paper is to find the structure ofthe linear operator preserving G-matrices on M۲.