REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

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dc.contributor.authorPąk, Karol-
dc.date.accessioned2015-12-06T19:05:19Z-
dc.date.available2015-12-06T19:05:19Z-
dc.date.issued2012-
dc.identifier.citationFormalized Mathematics, Volume 20, Issue 1, 2012, Pages 23-29-
dc.identifier.issn1426-2630-
dc.identifier.issn1898-9934-
dc.identifier.urihttp://hdl.handle.net/11320/3624-
dc.description.abstractWe introduce length-preserving linear transformations of Euclidean topological spaces. We also introduce rotation which preserves orientation (proper rotation) and reverses orientation (improper rotation). We show that every rotation that preserves orientation can be represented as a composition of base proper rotations. And finally, we show that every rotation that reverses orientation can be represented as a composition of proper rotations and one improper rotation.-
dc.language.isoen-
dc.publisherDe Gruyter Open-
dc.titleThe Rotation Group-
dc.typeArticle-
dc.identifier.doi10.2478/v10037-012-0004-2-
dc.description.AffiliationInstitute of Informatics, University of Białystok, Poland-
dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.-
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.-
dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.-
dc.description.referencesGrzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.-
dc.description.referencesCzesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.-
dc.description.referencesCzesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.-
dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.-
dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
dc.description.referencesCzesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.-
dc.description.referencesAgata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.-
dc.description.referencesKrzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.-
dc.description.referencesKatarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.-
dc.description.referencesKatarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.-
dc.description.referencesArtur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in En/T. Formalized Mathematics, 12(3):301-306, 2004.-
dc.description.referencesJarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.-
dc.description.referencesJarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.-
dc.description.referencesEugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.-
dc.description.referencesAnna Lango and Grzegorz Bancerek. Product of families of groups and vector spaces. Formalized Mathematics, 3(2):235-240, 1992.-
dc.description.referencesMichał Muzalewski. Categories of groups. Formalized Mathematics, 2(4):563-571, 1991.-
dc.description.referencesYatsuka Nakamura. Determinant of some matrices of field elements. Formalized Mathematics, 14(1):1-5, 2006, doi:10.2478/v10037-006-0001-4.-
dc.description.referencesBeata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.-
dc.description.referencesKarol Pąk. Basic properties of determinants of square matrices over a field. Formalized Mathematics, 15(1):17-25, 2007, doi:10.2478/v10037-007-0003-x.-
dc.description.referencesKarol 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.-
dc.description.referencesKarol Pąk. Block diagonal matrices. Formalized Mathematics, 16(3):259-267, 2008, doi:10.2478/v10037-008-0031-1.10.2478/v10037-008-0031-1-
dc.description.referencesKarol Pąk. Linear transformations of Euclidean topological spaces. Formalized Mathematics, 19(2):103-108, 2011, doi: 10.2478/v10037-011-0016-3.-
dc.description.referencesNobuyuki Tamura and Yatsuka Nakamura. Determinant and inverse of matrices of real elements. Formalized Mathematics, 15(3):127-136, 2007, doi:10.2478/v10037-007-0014-7.-
dc.description.referencesAndrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.-
dc.description.referencesAndrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.-
dc.description.referencesWojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.-
dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.-
dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.-
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.-
dc.description.referencesYuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.-
dc.description.referencesXiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.-
dc.description.referencesKatarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.-
dc.description.referencesKatarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.-
Występuje w kolekcji(ach):Artykuły naukowe (WInf)
Formalized Mathematics, 2012, Volume 20, Issue 1

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