Tridiagonal normal forms for orthogonal similarity classes of symmetric matrices

doi:10.1016/j.laa.2003.12.038

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	Tridiagonal normal forms for orthogonal similarity classes of symmetric matrices
	Dokovic, DZ ; Zhao, KM
	2004-06-01
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	384 页码:77-84
摘要	Let F be an algebraically closed field of characteristic different from 2. Define the orthogonal group, O-n (F), as the group of n by n matrices X over F such that XX' = I-n, where X' is the transpose of X and In the identity matrix. We show that every n by n symmetric matrix over F is orthogonally similar to a tridiagonal symmetric matrix. If further the characteristic is 0, we construct the tridiagonal normal form for the O-n (F)- similarity classes of symmetric matrices. We point out that, in this case, the known normal forms (as presented in the well known book by Gantmacher) are not tridiagonal. (C) 2004 Elsevier Inc. All rights reserved.
关键词	orthogonal group symmetric matrices tridiagonal matrices symmetrized Jordan blocks
DOI	10.1016/j.laa.2003.12.038
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000221592100006
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/19143
专题	中国科学院数学与系统科学研究院
通讯作者	Dokovic, DZ
作者单位	1.Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada 2.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Dokovic, DZ,Zhao, KM. Tridiagonal normal forms for orthogonal similarity classes of symmetric matrices[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2004,384:77-84.
APA	Dokovic, DZ,&Zhao, KM.(2004).Tridiagonal normal forms for orthogonal similarity classes of symmetric matrices.LINEAR ALGEBRA AND ITS APPLICATIONS,384,77-84.
MLA	Dokovic, DZ,et al."Tridiagonal normal forms for orthogonal similarity classes of symmetric matrices".LINEAR ALGEBRA AND ITS APPLICATIONS 384(2004):77-84.