Denote by 𝒦n(F) the linear space of all
n×n
alternate matrices over a field F. We first characterize all linear bijective maps on 𝒦n(F)(n≥4) preserving rank 2 when F is any field, and thereby the characterization of all linear bijective maps on 𝒦n(F) preserving the max-rank is done when F is any field
except for {0,1}
. Furthermore, the linear preservers of the determinant (resp., adjoint) on
𝒦n(F) are also characterized by
reducing them to the linear preservers of the max-rank when n
is even and F
is any field except for {0,1}. This paper can be viewed as a supplement version of several related results.