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