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Denote by &#x1D4A6;n(F) the linear space of all n×n alternate matrices over a field F. We first characterize all linear bijective maps on &#x1D4A6;n(F)(n≥4) preserving rank 2 when F is any field, and thereby the characterization of all linear bijective maps on &#x1D4A6;n(F) preserving the max-rank is done when F is any fieldexcept for {0,1}. Furthermore, the linear preservers of the determinant (resp., adjoint) on &#x1D4A6;n(F) are also characterized byreducing 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

Linear maps preserving rank 2 on the space of alternate matrices and their applications