Linear preservers on matrices

Abstract

Let U denote either the vector space of n×n matrices or the vector space of n×n symmetric matrices over an infinite field F. In this paper we characterize linear mappings L on U that satisfy one of the following properties: (i) L(adjA)=adjL(A) for all A in U; (ii) L preserves idempotent matrices, and L(In)=In, where F is the real field R or the complex field C; (iii) L(eA)=eL(A) for all A in U, where F=R or C. © 1987.