Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution
Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution作者机构:School of Mathematics Changsha University of Science & Technology Changsha 410076 P. R. China
出 版 物:《Acta Mathematica Sinica,English Series》 (数学学报(英文版))
年 卷 期:2007年第23卷第1期
页 面:95-102页
核心收录:
学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金:the National Natural Science Foundation of China Grant #10271021
主 题:division ring with involution hermitian inatrix adjacency geometry of matrices
摘 要:Let D be any division ring with an involution,Hn (D) be the space of all n × n hermitian matrices over D. Two hermitian matrices A and B are said to be adjacent if rank(A - B) = 1. It is proved that if φ is a bijective map from Hn(D)(n ≥ 2) to itself such that φ preserves the adjacency, then φ^-1 also preserves the adjacency. Moreover, if Hn(D) ≠J3(F2), then φ preserves the arithmetic distance. Thus, an open problem posed by Wan Zhe-Xian is answered for geometry of symmetric and hermitian matrices.