Linear preservers of circulant majorization onRn

Let M n , m be the set of all n × m real matrices. An n × n real matrix A is called circulant doubly stochastic if it is a convex combination of circulant permutation matrices. For x , y ∈ R n , x is said to be circulant majorized by y (written as x ≺ c y ), if there exists a circulant doubly stochastic matrix D such that x = D y . In this paper, the concept of circulant majorization is investigated and then the linear preservers and strong linear preservers of this concept are characterized on R n .