Generalized Doubly Stochastic Matrices and Linear Preservers of D-majorization

D-majorization is a group-induced cone ordering on R n induced by group G = { c P : c ∈ { - 1 , 1 } , P ∈ P ( n ) } , where P ( n ) is the set of all n -by- n permutation matrices. For x , y ∈ R n , x is said to be D-majorized by y (denoted by x ≺ D y ) if there exists some D ∈ Conv ( G ) such that x = D y . In the present paper, the concept of D-majorization is studied and then the linear preservers of this concept are characterized.