On Linear Maps Preserving g-Majorization from n to m

Let [superscript]...n[/superscript] and [subscript]...m[/subscript] be the usual spaces of n-dimensional column and m-dimensional row vectors on ... , respectively, where ... is the field of real or complex numbers. In this paper, the relations gs-majorization, lgw-majorization, and rgw-majorization are considered on [superscript]...n[/superscript] and [subscript]...m[/subscript] . Then linear maps T:[superscript]...n[/superscript] [arrow right][superscript]...m[/superscript] preserving lgw-majorization or gs-majorization and linear maps S:[subscript]...n[/subscript] [arrow right][subscript]...m[/subscript] , preserving rgw-majorization are characterized.