W BIAŁYMSTOKU
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http://hdl.handle.net/11320/15404Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Okazaki, Hiroyuki | - |
| dc.date.accessioned | 2023-10-09T11:17:23Z | - |
| dc.date.available | 2023-10-09T11:17:23Z | - |
| dc.date.issued | 2023 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 31, Issue 1, Pages 53-57 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/15404 | - |
| dc.description.abstract | In this article, we formalize the Gram-Schmidt process in the Mizar system [2], [3] (compare another formalization using Isabelle/HOL proof assistant [1]). This process is one of the most famous methods for orthonormalizing a set of vectors. The method is named after Jørgen Pedersen Gram and Erhard Schmidt [4]. There are many applications of the Gram-Schmidt process in the field of computer science, e.g., error correcting codes or cryptology [8]. First, we prove some preliminary theorems about real unitary space. Next, we formalize the definition of the Gram-Schmidt process that finds orthonormal basis. We followed [5] in the formalization, continuing work developed in [7], [6]. | 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 | Gram-Schmidt process | pl |
| dc.subject | orthonormal basis | pl |
| dc.subject | linear algebra | pl |
| dc.title | On the Formalization of Gram-Schmidt Process for Orthonormalizing a Set of Vectors | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2023 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2023-0005 | - |
| dc.description.Affiliation | Shinshu University, Nagano, Japan | pl |
| dc.description.references | Jesus Aransay and Jose Divasón. A formalisation in HOL of the fundamental theorem of linear algebra and its application to the solution of the least squares problem. Journal of Automated Reasoning, 58(4):509–535, 2017. doi:10.1007/s10817-016-9379-z. | 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 | Ward Cheney and David Kincaid. Linear Algebra: Theory and Applications. Jones and Bartlett publishers, 2009. | pl |
| dc.description.references | David G. Luenberger. Optimization by Vector Space Methods. John Wiley and Sons, 1969. | pl |
| dc.description.references | Kazuhisa Nakasho, Hiroyuki Okazaki, and Yasunari Shidama. Real vector space and related notions. Formalized Mathematics, 29(3):117–127, 2021. doi:10.2478/forma-2021-0012. | pl |
| dc.description.references | Hiroyuki Okazaki. Formalization of orthogonal decomposition for Hilbert spaces. Formalized Mathematics, 30(4):295–299, 2022. doi:10.2478/forma-2022-0023. | pl |
| dc.description.references | Rene Thiemann and Akihisa Yamada. Formalizing Jordan Normal Forms in Isabelle/HOL. In Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, pages 88–99, New York, NY, USA, 2016. Association for Computing Machinery. ISBN 9781450341271. doi:10.1145/2854065.2854073. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 31 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 53 | pl |
| dc.description.lastpage | 57 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2023, Volume 31, Issue 1 | |
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|---|---|---|---|---|
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