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 |
| DOI | 10.1016/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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