中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
Normal forms for orthogonal similarity classes of skew-symmetric matrices

文献类型:期刊论文

作者Pokovivic, Dragomir Z.; Rietsch, Konstanze; Zhao, Kaiming
刊名JOURNAL OF ALGEBRA
出版日期2007-02-15
卷号308期号:2页码:686-703
关键词orthogonal group skew-symmetric matrices bidiagonal matrices tridiagonal matrices
ISSN号0021-8693
DOI10.1016/j.jalgebra.2006.09.006
英文摘要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.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000244704100014
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/5225]  
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.

入库方式: OAI收割

来源:数学与系统科学研究院

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