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 = {cP : c is an element of {-1, 1}, P is an element of P(n)}, where P(n) is the set of all n-by-n permutationmatrices. For x, y is an element of R-n, x is said to be D-majorized by y (denoted by x <(D) y) if there exists some D is an element of Conv(G) such that x = Dy. In the present paper, the concept of D-majorization is studied and then the linear preservers of this concept are characterized.