Linear preservers of minimal rank
Linear maps of upper triangular matrices preserving properties related to completion problems are studied. It is proved for a linear transformation on the vector space of upper triangular matrices that mapping the matrices of minimal rank 1 into itself and either having the analogous property with respect to matrices of full minimal rank or being bijective, is a triangular equivalence or a triangular equivalence follows after some steps. Examples including transformation of triangular similarity are added. The connection with the paper by \textit{M. Marcus} and \textit{B. N. Moyls} [Pacific J. Math. 9, 1215-1221 (1959; Zbl 0089.08902)] on rank preservers is mentioned.
scientific article; zbMATH DE number 1453253