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Topologies on quotient space of matrices via semi-tensor product
Cheng, Daizhan1; Liu, Zequn1,2
2019-09-01
Source PublicationASIAN JOURNAL OF CONTROL
ISSN1561-8625
Pages10
AbstractAn 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.
Keywordequivalence class metric topology product topology quotient space quotient topology semi-tensor product
DOI10.1002/asjc.2156
Language英语
Funding ProjectNational Natural Science Foundation of China[61333001] ; National Natural Science Foundation of China[61733018] ; National Natural Science Foundation of China[61773371]
WOS Research AreaAutomation & Control Systems
WOS SubjectAutomation & Control Systems
WOS IDWOS:000484482600001
PublisherWILEY
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/33316
Collection系统科学研究所
Corresponding AuthorCheng, Daizhan
Affiliation1.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
Recommended Citation
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.
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