Geometry of skew-Hermitian matrices

doi:10.1016/j.laa.2004.08.030

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	Geometry of skew-Hermitian matrices
	Huang, LP ; Wan, ZX
	2005-02-01
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	396 页码:127-157
摘要	Let D be a division ring with an involution (-). Assume that F = {a is an element of D : a = (a) over bar)} is a proper subfield of D and is contained in the center of D. Let I H-n be the set of n x n skew-Hermitian matrices over D. If H-1, H-2 is an element of I H-n (D) and rank (H-1 - H-2) = 1, H-1 and H-2 are said to be adjacent. The fundamental theorem of the geometry of skew-Hermitian matrices over D is proved: Let n greater than or equal to 2 and A be a bijective map of Y H-n (D) to itself, which preserves the adjacency. Then A is of the form A (X) = alpha (t)(P) over tildeX(sigma) P + H-0 For AllX is an element of I H-n (D), where alpha is an element of F*, P is an element of GL(n) (D), H-0 is an element of I H-n (D), and sigma is an automorphism of D. (C) 2004 Elsevier Inc. All rights reserved.
关键词	geometry of matrices skew-Hermitian matrix adjacency division ring with an involution division ring of generalized quaternions
DOI	10.1016/j.laa.2004.08.030
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000226476600007
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1713
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, LP
作者单位	1.Changshsa Univ Sci & Technol, Sch Math & Comp Sci, Changsha 410076, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Suzhou Univ, Inst Math, Suzhou 215006, Peoples R China
推荐引用方式 GB/T 7714	Huang, LP,Wan, ZX. Geometry of skew-Hermitian matrices[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2005,396:127-157.
APA	Huang, LP,&Wan, ZX.(2005).Geometry of skew-Hermitian matrices.LINEAR ALGEBRA AND ITS APPLICATIONS,396,127-157.
MLA	Huang, LP,et al."Geometry of skew-Hermitian matrices".LINEAR ALGEBRA AND ITS APPLICATIONS 396(2005):127-157.