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http://hdl.handle.net/11320/12388
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Pole DC | Wartość | Język |
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dc.contributor.author | Nakasho, Kazuhisa | - |
dc.contributor.author | Okazaki, Hiroyuki | - |
dc.contributor.author | Shidama, Yasunari | - |
dc.date.accessioned | 2022-01-04T06:38:42Z | - |
dc.date.available | 2022-01-04T06:38:42Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Formalized Mathematics, Volume 29, Issue 3, Pages 117-127 | pl |
dc.identifier.issn | 1426–2630 | - |
dc.identifier.uri | http://hdl.handle.net/11320/12388 | - |
dc.description | This study was supported in part by JSPS KAKENHI Grant Numbers 17K00182 and 20K19863. | pl |
dc.description.abstract | In this paper, we discuss the properties that hold in finite dimensional vector spaces and related spaces. In the Mizar language [1], [2], variables are strictly typed, and their type conversion requires a complicated process. Our purpose is to formalize that some properties of finite dimensional vector spaces are preserved in type transformations, and to contain the complexity of type transformations into this paper. Specifically, we show that properties such as algebraic structure, subsets, finite sequences and their sums, linear combination, linear independence, and affine independence are preserved in type conversions among TOP-REAL(n), REAL-NS(n), and n-VectSp over F Real. We referred to [4], [9], and [8] in the formalization. | pl |
dc.language.iso | en | pl |
dc.publisher | DeGruyter Open | pl |
dc.subject | real vector space | pl |
dc.subject | topological space | pl |
dc.subject | normed spaces | pl |
dc.title | Real Vector Space and Related Notions | pl |
dc.type | Article | pl |
dc.rights.holder | © 2021 University of Białymstoku | pl |
dc.rights.holder | CC-BY-SA License ver. 3.0 or later | pl |
dc.identifier.doi | 10.2478/forma-2021-0012 | - |
dc.description.Affiliation | Kazuhisa Nakasho - Yamaguchi University, Yamaguchi, Japan | pl |
dc.description.Affiliation | Hiroyuki Okazaki - Shinshu University, Nagano, Japan | pl |
dc.description.Affiliation | Yasunari Shidama - Shinshu University, Nagano, Japan | pl |
dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8-17. | pl |
dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6. | pl |
dc.description.references | Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577–580, 2005. | pl |
dc.description.references | Miyadera Isao. Functional Analysis. Riko-Gaku-Sya, 1972. | pl |
dc.description.references | Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339–345, 1996. | pl |
dc.description.references | Karol Pąk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199–211, 2007. doi:10.2478/v10037-007-0024-5. | pl |
dc.description.references | Karol Pąk. Linear map of matrices. Formalized Mathematics, 16(3):269–275, 2008. doi:10.2478/v10037-008-0032-0. | pl |
dc.description.references | Laurent Schwartz. Theorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997. | pl |
dc.description.references | Kosaku Yosida. Functional Analysis. Springer, 1980. | pl |
dc.identifier.eissn | 1898-9934 | - |
dc.description.volume | 29 | pl |
dc.description.issue | 3 | pl |
dc.description.firstpage | 117 | pl |
dc.description.lastpage | 127 | pl |
dc.identifier.citation2 | Formalized Mathematics | pl |
Występuje w kolekcji(ach): | Formalized Mathematics, 2021, Volume 29, Issue 3 |
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10.2478_forma-2021-0012.pdf | 284,25 kB | Adobe PDF | Otwórz |
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