International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 63, Pages 3409-3417

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

Chongguang Cao and Xiaomin Tang

Department of Mathematics, Heilongjiang University, Harbin 150080, China

Received 18 January 2004

Copyright © 2004 Chongguang Cao and Xiaomin Tang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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)(n4) 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.