International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 61-64, Pages 3409-3417
doi:10.1155/S0161171204401161

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

Abstract

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.