Topologies on quotient space of matrices via semi-tensor product

doi:10.1002/asjc.2156

CSpace > 系统科学研究所

	Topologies on quotient space of matrices via semi-tensor product
	Cheng, Daizhan1 ; Liu, Zequn 1,2
	2019-09-01
发表期刊	ASIAN JOURNAL OF CONTROL
ISSN	1561-8625
页码	10
摘要	An equivalence of matrices via semi-tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices lead to the product topology and quotient topology respectively. Then the Frobenious inner product of matrices is extended to equivalence classes, which produces a metric on the quotient space. This metric leads to a metric topology. A comparison for these three topologies is presented. Some topological properties are revealed.
关键词	equivalence class metric topology product topology quotient space quotient topology semi-tensor product
DOI	10.1002/asjc.2156
语种	英语
资助项目	National Natural Science Foundation of China[61333001] ; National Natural Science Foundation of China[61733018] ; National Natural Science Foundation of China[61773371]
WOS研究方向	Automation & Control Systems
WOS类目	Automation & Control Systems
WOS记录号	WOS:000484482600001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/33316
专题	系统科学研究所
通讯作者	Cheng, Daizhan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Daizhan,Liu, Zequn. Topologies on quotient space of matrices via semi-tensor product[J]. ASIAN JOURNAL OF CONTROL,2019:10.
APA	Cheng, Daizhan,&Liu, Zequn.(2019).Topologies on quotient space of matrices via semi-tensor product.ASIAN JOURNAL OF CONTROL,10.
MLA	Cheng, Daizhan,et al."Topologies on quotient space of matrices via semi-tensor product".ASIAN JOURNAL OF CONTROL (2019):10.