Strong linear preservers of rank reverse permutability on triangular matrices

Let F be a field with vertical bar F1 vertical bar > 2 and T-n(F) be the set of all n x n upper triangular matrices, where n >= 2. Let k >= 2 be a given integer. A k-tuple of matrices A(1),..., A(k) is an element of T-n (F) is called rank reverse permutable if rank (A(1)A(2)... A(k)) = rank(A(k)A(k- 1)... A(1)). We characterize the linear maps on T-n (F) that strongly preserve the set of rank reverse permutable matrix k-tuples. (c) 2005 Elsevier Inc. All rights reserved.