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`Abstract and Applied AnalysisVolume 2014, Article ID 596756, 5 pageshttp://dx.doi.org/10.1155/2014/596756`
Research Article

## Induced Maps on Matrices over Fields

1Department of Foundation, Harbin Finance University, Harbin 150030, China
2School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 21 October 2013; Revised 23 December 2013; Accepted 2 January 2014; Published 26 February 2014

Academic Editor: Chi-Keung Ng

Copyright © 2014 Li Yang 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.

#### Abstract

Suppose that is a field and are integers. Denote by the set of all matrices over and by the set . Let () be functions on , where stands for the set . We say that a map is induced by if is defined by . We say that a map on preserves similarity if , where represents that and are similar. A map on preserving inverses of matrices means for every invertible . In this paper, we characterize induced maps preserving similarity and inverses of matrices, respectively.