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Abstract and Applied Analysis
Volume 2013, Article ID 581683, 8 pages
Research Article

A Note on -Potence Preservers on Matrix Spaces over Complex Field

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China

Received 13 March 2013; Accepted 3 May 2013

Academic Editor: Chunrui Zhang

Copyright © 2013 Xiaofei Song et al. 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.


Let be the field of all complex numbers, the space of all matrices over , and the subspace of consisting of all symmetric matrices. The map satisfies that is -potent in implying that is -potent in , where then there exist an invertible matrix and with such that for every . Moreover, the inductive method used in this paper can be used to characterise similar maps from to .