Advances in Analysis and Geometry: New Developments Using Clifford Algebras
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2004
|
| Schriftenreihe: | Trends in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations ·2 ·2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized complex numbers (hypercomplex numbers) of the form a + bi + cj. It hence took him a long time to accept that a fourth dimension was necessary and that commutativity couldn't be kept and he wondered about a possible real life meaning of this fourth dimension which he identified with the scalar part qo as opposed to the vector part ql i + q2j + q3k which represents a point in space |
| Beschreibung: | 1 Online-Ressource (XV, 376 p) |
| ISBN: | 9783034878388 9783034895897 |
| DOI: | 10.1007/978-3-0348-7838-8 |
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| 500 | |a On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations ·2 ·2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized complex numbers (hypercomplex numbers) of the form a + bi + cj. It hence took him a long time to accept that a fourth dimension was necessary and that commutativity couldn't be kept and he wondered about a possible real life meaning of this fourth dimension which he identified with the scalar part qo as opposed to the vector part ql i + q2j + q3k which represents a point in space | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Qian, Tao |
| author_facet | Qian, Tao |
| author_role | aut |
| author_sort | Qian, Tao |
| author_variant | t q tq |
| building | Verbundindex |
| bvnumber | BV042421966 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184415478 (DE-599)BVBBV042421966 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7838-8 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034878388 9783034895897 |
| language | English |
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| spelling | Qian, Tao Verfasser aut Advances in Analysis and Geometry New Developments Using Clifford Algebras edited by Tao Qian, Thomas Hempfling, Alan McIntosh, Frank Sommen Basel Birkhäuser Basel 2004 1 Online-Ressource (XV, 376 p) txt rdacontent c rdamedia cr rdacarrier Trends in Mathematics On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations ·2 ·2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized complex numbers (hypercomplex numbers) of the form a + bi + cj. It hence took him a long time to accept that a fourth dimension was necessary and that commutativity couldn't be kept and he wondered about a possible real life meaning of this fourth dimension which he identified with the scalar part qo as opposed to the vector part ql i + q2j + q3k which represents a point in space Mathematics Global analysis (Mathematics) Integral equations Operator theory Functions, special Number theory Mathematical physics Analysis Integral Equations Operator Theory Special Functions Number Theory Mathematical Methods in Physics Mathematik Mathematische Physik Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Clifford-Analysis (DE-588)4484012-3 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Differentialgeometrie (DE-588)4012248-7 s Clifford-Algebra (DE-588)4199958-7 s 2\p DE-604 Clifford-Analysis (DE-588)4484012-3 s 3\p DE-604 Hempfling, Thomas Sonstige oth McIntosh, Alan Sonstige oth Sommen, Frank Sonstige oth https://doi.org/10.1007/978-3-0348-7838-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Qian, Tao Advances in Analysis and Geometry New Developments Using Clifford Algebras Mathematics Global analysis (Mathematics) Integral equations Operator theory Functions, special Number theory Mathematical physics Analysis Integral Equations Operator Theory Special Functions Number Theory Mathematical Methods in Physics Mathematik Mathematische Physik Clifford-Algebra (DE-588)4199958-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| subject_GND | (DE-588)4199958-7 (DE-588)4012248-7 (DE-588)4484012-3 (DE-588)4143413-4 |
| title | Advances in Analysis and Geometry New Developments Using Clifford Algebras |
| title_auth | Advances in Analysis and Geometry New Developments Using Clifford Algebras |
| title_exact_search | Advances in Analysis and Geometry New Developments Using Clifford Algebras |
| title_full | Advances in Analysis and Geometry New Developments Using Clifford Algebras edited by Tao Qian, Thomas Hempfling, Alan McIntosh, Frank Sommen |
| title_fullStr | Advances in Analysis and Geometry New Developments Using Clifford Algebras edited by Tao Qian, Thomas Hempfling, Alan McIntosh, Frank Sommen |
| title_full_unstemmed | Advances in Analysis and Geometry New Developments Using Clifford Algebras edited by Tao Qian, Thomas Hempfling, Alan McIntosh, Frank Sommen |
| title_short | Advances in Analysis and Geometry |
| title_sort | advances in analysis and geometry new developments using clifford algebras |
| title_sub | New Developments Using Clifford Algebras |
| topic | Mathematics Global analysis (Mathematics) Integral equations Operator theory Functions, special Number theory Mathematical physics Analysis Integral Equations Operator Theory Special Functions Number Theory Mathematical Methods in Physics Mathematik Mathematische Physik Clifford-Algebra (DE-588)4199958-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Integral equations Operator theory Functions, special Number theory Mathematical physics Analysis Integral Equations Operator Theory Special Functions Number Theory Mathematical Methods in Physics Mathematik Mathematische Physik Clifford-Algebra Differentialgeometrie Clifford-Analysis Aufsatzsammlung |
| url | https://doi.org/10.1007/978-3-0348-7838-8 |
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