Similarity reduction of matrix over a quaternion division ring

doi:10.1016/j.laa.2007.08.006

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	Similarity reduction of matrix over a quaternion division ring
	Huang, Li-Ping 1; Liu, Zhuo-Jun2
	2008-02-01
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	428 期号:4 页码:765-780
摘要	Let F be a field of characteristic not equal 2, H-F = (a,b/F) the quaternion division ring over F. This paper discusses the similarity of polynomials over HF. By using polynomials over H-F, this paper proves that every square matrix over H-F is similar to a uniquely generalized Jordan canonical form, and a quaternion matrix A is similar to a matrix over F if and only if A is similar to A* via a Hermite similarity transformation, or if and only if A is product of two quaternion Hermite matrices. (C) 2007 Elsevier Inc. All rights reserved.
关键词	quaternion division ring matrix polynomial similarity centralizable matrix generalized Jordan canonical form
DOI	10.1016/j.laa.2007.08.006
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000253307800006
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/4581
专题	系统科学研究所
通讯作者	Huang, Li-Ping
作者单位	1.Changsha 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
推荐引用方式 GB/T 7714	Huang, Li-Ping,Liu, Zhuo-Jun. Similarity reduction of matrix over a quaternion division ring[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2008,428(4):765-780.
APA	Huang, Li-Ping,&Liu, Zhuo-Jun.(2008).Similarity reduction of matrix over a quaternion division ring.LINEAR ALGEBRA AND ITS APPLICATIONS,428(4),765-780.
MLA	Huang, Li-Ping,et al."Similarity reduction of matrix over a quaternion division ring".LINEAR ALGEBRA AND ITS APPLICATIONS 428.4(2008):765-780.