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http://hdl.handle.net/11320/17797Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Schwarzweller, Christoph | - |
| dc.contributor.author | Rowińska-Schwarzweller, Agnieszka | - |
| dc.date.accessioned | 2025-01-10T08:27:06Z | - |
| dc.date.available | 2025-01-10T08:27:06Z | - |
| dc.date.issued | 2024 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 32, Issue 1, Pages 223–233 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/17797 | - |
| dc.description.abstract | In this article, using the Mizar system, we introduce some standard examples of vector spaces, e.g., the vector space of linear transformations between vector spaces. We formulate some conditions for the isomorphism of finite-dimensional vector spaces and prove that linear transformations are uniquely determined by their values with respect to the basis. | pl |
| dc.language.iso | en | pl |
| dc.publisher | DeGruyter Open | pl |
| dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
| dc.subject | vector space | pl |
| dc.subject | linear transformation | pl |
| dc.subject | dimension of a vector space | pl |
| dc.title | Some Standard Examples of Vector Spaces | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2024 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2024-0019 | - |
| dc.description.Affiliation | Christoph Schwarzweller - Institute of Informatics, University of Gdańsk, Poland | pl |
| dc.description.Affiliation | Agnieszka Rowińska-Schwarzweller - Institute of Informatics, University of Gdańsk, Poland | pl |
| dc.description.references | Jesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137–142, 2007. doi:10.2478/v10037-007-0015-6. | 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 | Norbert Christmann. Einführung in die (lineare) Algebra. Lecture Notes, University of Kaiserslautern, Germany, 1989. | pl |
| dc.description.references | Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363–371, 2016. doi:10.15439/2016F520. | pl |
| dc.description.references | I. Martin Isaacs. Algebra, A Graduate Course. American Mathematical Society, 2009. | pl |
| dc.description.references | Serge Lang. Algebra (Revised Third Edition). Springer Verlag, 2002. | pl |
| dc.description.references | Christoph Schwarzweller. Normal extensions. Formalized Mathematics, 31(1):121–130, 2023. doi:10.2478/forma-2023-0011. | pl |
| dc.description.references | Yasushige Watase. Ring of endomorphisms and modules over a ring. Formalized Mathematics, 30(3):211–221, 2022. doi:10.2478/forma-2022-0016. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 32 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 223 | pl |
| dc.description.lastpage | 233 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0001-9587-8737 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2024, Volume 32, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Some-Standard-Examples-of-Vector-Spaces.pdf | 268,79 kB | Adobe PDF | Otwórz |
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