Normal forms for orthogonal similarity classes of skew-symmetric matrices

doi:10.1016/j.jalgebra.2006.09.006

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	Normal forms for orthogonal similarity classes of skew-symmetric matrices
	Pokovivic, Dragomir Z.; Rietsch, Konstanze ; Zhao, Kaiming
	2007-02-15
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	308 期号:2 页码:686-703
摘要	Let F be an algebraically closed field of characteristic different from 2. Define the orthogonal group, On (F), as the group of n by it matrices X over F such that XX' = In, where X' is the transpose of X and In the identity matrix. We show that every nonsingular n by n skew-symmetric matrix over F is orthogonally similar to a bidiagonal skew-symmetric matrix. In the singular case one has to allow some 4-diagonal blocks as well. If further the characteristic is 0, we construct the normal form for the O-n(F)-similarity classes of skew-symmetric matrices. In this case, the known normal forms (as presented in the well-known book by Gantmacher) are quite different. Finally we study some related varieties of matrices. We prove that the variety of normalized nilpotent n by n bidiagonal matrices for n = 2s + 1 is irreducible of dimension s. As a consequence the skew-symmetric nilpotent n by n bidiagonal matrices are shown to form a variety of pure dimensions. (c) 2006 Elsevier Inc. All rights reserved.
关键词	orthogonal group skew-symmetric matrices bidiagonal matrices tridiagonal matrices
DOI	10.1016/j.jalgebra.2006.09.006
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000244704100014
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5226
专题	中国科学院数学与系统科学研究院
通讯作者	Rietsch, Konstanze
作者单位	1.Kings Coll London, Dept Math, London WC2R 2LS, England 2.Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada 3.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Pokovivic, Dragomir Z.,Rietsch, Konstanze,Zhao, Kaiming. Normal forms for orthogonal similarity classes of skew-symmetric matrices[J]. JOURNAL OF ALGEBRA,2007,308(2):686-703.
APA	Pokovivic, Dragomir Z.,Rietsch, Konstanze,&Zhao, Kaiming.(2007).Normal forms for orthogonal similarity classes of skew-symmetric matrices.JOURNAL OF ALGEBRA,308(2),686-703.
MLA	Pokovivic, Dragomir Z.,et al."Normal forms for orthogonal similarity classes of skew-symmetric matrices".JOURNAL OF ALGEBRA 308.2(2007):686-703.