© Hindawi Publishing Corp. LINEAR MAPS PRESERVING RANK 2 ON THE SPACE OF ALTERNATE MATRICES AND THEIR APPLICATIONS

Denote by n(F) the linear space of all n×n alternate matrices over a field F. We first characterize all linear bijective maps on n(F) (n ≥ 4) preserving rank 2 when F is any field, and thereby the characterization of all linear bijective maps on n(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 n(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. 2000 Mathematics Subject Classification: 15A03, 15A04