Additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra  

作　　者：HAN Jing-wen ZHENG Bao-dong 

机构地区：[1]Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China [2]Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

出　　处：《Chinese Quarterly Journal of Mathematics》2007年第4期482-491,共10页数学季刊（英文版）

基　　金：Supported by NSF of China(10571033)

摘　　要：Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.

关 键 词：additive map quaternion division algebra Hermitian matrix RANK 

分 类 号：O151.2[理学—数学]