Linear preservers of minimal rank

It is proved that a linear transformation on the vector space of upper tria ngular matrices that maps the set of matrices of minimal rank 1 into itself , and either has the analogous property with respect to matrices of full mi nimal rank, or is bijective, is a triangular equivalence, or a Aip about th e south-west north-east diagonal followed by a triangular equivalence, The result can be regarded as an analogue of Marcus-Moyls theorem in the contex t of triangular matrices. (C) 2000 Elsevier Science Inc. All rights reserve d.