A vector x ∈Rn is weakly k-majorized by a vector q ∈ Rk if the sum of r largest components of x is less than or equal to the sum of r largest components of q for r = 1,2,…,k and k ≤ n. In this paper we extend the components of x to their absolute values in the above description and generalize some results by Dahl and Margot.
