Rank 2 preservers on symmetric matrices with zero trace

Abstract

Let F be a field, V1 and V2 be vector spaces of matrices over F and let ρ be the rank function. If T :V1 → V2 is a linear map, and k a fixed positive integer, we say that T is a rank k preserver if for any matrix Aϵ, V1 ρ(A) = k implies ρ(T( A))= k . In this paper, we characterize those rank 2 preservers on symmetric matrices with zero trace under certain conditions.