Linear preservers on triangular matrices

Let T-n(F) denote the vector space of all n x n upper triangular matrices over a field F. We characterize those linear transformations T on T-n(F) that satisfy one of the following properties: (1) T preserves rank one matrices; (2) T preserves both singular and nonsingular matrices; (3) T is nonsingular and T(adj A) = adj T(A) for all A is an element of T-n(F). (C) 1998 Elsevier Science Inc.