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Let  F  be a field,  V  1  and  V  2  be vector spaces of matrices over  F  and let ρ be the rank function. If  T  :V 1  →  V  2  is a linear map, and  k  a fixed positive integer, we say that  T  is a rank  k  preserver if for any matrix  A ϵ,  V  1  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.

Rank 2 preservers on symmetric matrices with zero trace