On Linear Maps Preserving g-Majorization from to

Let Open image in new window and Open image in new window be the usual spaces of n-dimensional column and m-dimensional row vectors on Open image in new window , respectively, where Open image in new window is the field of real or complex numbers. In this paper, the relations gs-majorization, lgw-majorization, and rgw-majorization are considered on Open image in new window and Open image in new window . Then linear maps Open image in new window preserving lgw-majorization or gs-majorization and linear maps Open image in new window , preserving rgw-majorization are characterized.