Adjacency preserving bijection maps of hermitian matrices over any division ring with an involution

作者：Huang; Li Ping

来源：Acta Mathematica Sinica-English Series, 2007, 23(1): 95-102.

DOI：10.1007/s10114-005-0770-7

• division ring with involution
• hermitian matrix
• adjacency
• geometry of matrices

Let D be any division ring with an involution, de,, (D) be the space of all n x 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 W is a bijective map from H,(D)(n >= 2) to itself such that phi preserves the adjacency, then phi(-1) also preserves the adjacency. Moreover, if H-n(D) not equal phi(3)(F-2), then W preserves the arithmetic distance. Thus, an open problem posed by Wan Zhe-Xian is answered for geometry of symmetric and hermitian matrices.

• 单位
  长沙学院