Strong linear preservers of rank reverse permutability on triangular matrices

Let F be a field with F > 2 and Tn(F) be the set of all n × n upper triangular matrices, where n 2. Let k 2 be a given integer. A k-tuple of matrices A1, …, Ak Tn(F) is called rank reverse permutable if rank(A1 A2 Ak) = rank(Ak Ak−1 A1). We characterize the linear maps on Tn(F) that strongly preserve the set of rank reverse permutable matrix k-tuples.