Abstr. Appl. Anal. 2014 (SI52), 1-5, (2014) DOI: 10.1155/2014/596756
Li Yang, Xuezhi Ben, Ming Zhang, Chongguang Cao
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.