Linear/additive preservers of rank 2 on spaces of alternate matrices over fields Original Research Article

Let Kn(F) be the linear space of all n × n alternate matrices over a field F, and let image be its subset consisting of all rank-2 matrices. An operator phi : Kn(F) → Kn(F) is said to be additive if phi(A + B) = phi(A) + phi(B) for any A, B set membership, variant Kn(F), linear if phi is additive and phi(aA) = af(A) for every a set membership, variant F and A set membership, variant Kn(F), and a preserver of rank 2 on Kn(F) if image. When n greater-or-equal, slanted 4, we characterize all linear (respectively, additive) preservers of rank 2 on Kn(F) over any field (respectively, any field that is not isomorphic to a proper subfield of itself).