Topologies on quotient space of matrices via semi-tensor product

doi:10.1002/asjc.2156

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	Topologies on quotient space of matrices via semi-tensor product
	Cheng, Daizhan1 ; Liu, Zequn 1,2
刊名	ASIAN JOURNAL OF CONTROL
	2019-09-01
页码	10
关键词	equivalence class metric topology product topology quotient space quotient topology semi-tensor product
ISSN号	1561-8625
DOI	10.1002/asjc.2156
英文摘要	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.
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
语种	英语
出版者	WILEY
WOS记录号	WOS:000484482600001
内容类型	期刊论文
源URL	[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.