Linear maps preserving Drazin inverses of matrices over fields

Abstract

Let F be a field with at least five elements, M n ( F) the n × n full matrix algebra over F. In this paper, we determine the forms of linear maps from M n ( F) to M m ( F) preserving Drazin inverses of matrices under ch F ≠ 2 and m, n > 1, and also determine the forms of linear bijections from M n ( F) to itself preserving Drazin inverses of matrices under ch F = 2 and n > 1.