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.
Citation
Li Yang. Xuezhi Ben. Ming Zhang. Chongguang Cao. "Induced Maps on Matrices over Fields." Abstr. Appl. Anal. 2014 (SI52) 1 - 5, 2014. https://doi.org/10.1155/2014/596756