Some applications of semitensor product of matrices in algebra

doi:10.1016/j.camwa.2006.03.028

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	Some applications of semitensor product of matrices in algebra
	Cheng, Daizhan
	2006-09-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	52 期号:6-7 页码:1045-1066
摘要	A review on semitensor product (STP) of matrices is given. It is a generalization of the conventional matrix product for the case when the dimensions of the factor matrices do not satisfy the requirement. Using it, we investigate some structure-related properties of algebras. First, we consider when an algebra is a Lie algebra. The result reveals the topological structure of all finite-dimensional Lie algebras as the variety of a set of polynomial equations. Then we investigate the invertibility of algebras. Invertibility condition is expressed via STP. Finally, the tensor product of algebras is investigated. (c) 2006 Elsevier Ltd. All rights reserved.
关键词	semitensor product of matrices (Lie) algebra structure matrix
DOI	10.1016/j.camwa.2006.03.028
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000243017700021
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3546
专题	中国科学院数学与系统科学研究院
通讯作者	Cheng, Daizhan
作者单位	Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Daizhan. Some applications of semitensor product of matrices in algebra[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2006,52(6-7):1045-1066.
APA	Cheng, Daizhan.(2006).Some applications of semitensor product of matrices in algebra.COMPUTERS & MATHEMATICS WITH APPLICATIONS,52(6-7),1045-1066.
MLA	Cheng, Daizhan."Some applications of semitensor product of matrices in algebra".COMPUTERS & MATHEMATICS WITH APPLICATIONS 52.6-7(2006):1045-1066.