Linear transformations preserving sets of ranks
LeRoy B. Beasley · Rocky Mountain Journal of Mathematics · 1983
Let T be a linear transformation on M m ,"(F), the set of all m x n matrices over the algebraically closed field F, and let Rj denote the subset of all matrices of rank j.Further let R E = U/e£ Rj where E is a subset of {0,1, ..., min(m, n)}.We explore the structure of Twhen T(R E ) g R E .