Quaternions and Cayley numbers: algebra and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Academic Publishers
1997
|
| Series: | Mathematics and Its Applications
403 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 237 Seiten graph. Darst. |
| ISBN: | 0792345134 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quaternions and Cayley numbers |b algebra and applications |c by J. P. Ward, Department of Mathematical Sciences, Loughborough University, Loughborough, England |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Academic Publishers |c 1997 | |
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Record in the Search Index
| _version_ | 1804126130155814912 |
|---|---|
| adam_text | CONTENTS
Preface vii
1 Fundamentals of Linear Algebra
1.1 Integers, Rationals and Real Numbers 1
1.2 Real Numbers and Displacements 5
1.3 Groups 9
1.4 Rings and Fields 14
1.5 Linear Spaces 19
1.6 Inner Product Spaces 27
1.7 Algebras 38
1.8 Complex Numbers 42
2 Quaternions
2.1 Inventing Quaternions 54
2.2 Quaternion Algebra 62
2.3 The Exponential Form and Root Extraction 70
2.4 Frobenius Theorem 72
2.5 Inner Product for Quaternions 76
2.6 Quaternions and Rotations in 3 and 4 Dimensions 78
2.7 Relation to the Rotation Matrix 89
2.8 Matrix Formulation of Quaternions 91
2.9 Applications to Spherical Trigonometry 95
2.10 Rotating Axes in Mechanics 102
3 Complexified Quaternions
3.1 Scalars, Pseudoscalars, Vectors and Pseudovectors 105
3.2 Complexified Quaternions: Euclidean Metric 107
3.3 Complexified Quaternions: Minkowski Metric 114
3.4 Application of Complexified Quaternions to Space Time 120
3.5 Quaternions and Electromagnetism 133
3.6 Quaternionic Representation of Bivectors 139
3.7 Null Tetrad for Space time 146
3.8 Classification of Complex Bivectors and of the Weyl Tensor 158
vi
4 Cayley Numbers
4.1 A Common Notation for Numbers 164
4.2 Cayley Numbers 167
4.3 Angles and Cayley Numbers 173
4.4 Cayley Number Identities 177
4.5 Normed Algebras and the Hurwitz Theorem 183
4.6 Rotations in 7 and 8 Dimensional Euclidean Space 195
4.7 Basis Elements for Cayley Numbers 206
4.8 Geometry of 8 Dimensional Rotations 213
Appendix 1 Clifford Algebras 217
Appendix 2 Computer Algebra and Cayley Numbers 225
References 231
Index 233
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| id | DE-604.BV011600171 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:12:33Z |
| institution | BVB |
| isbn | 0792345134 |
| language | English |
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| physical | XI, 237 Seiten graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer Academic Publishers |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Ward, Joseph P. 1949- Verfasser (DE-588)173187439 aut Quaternions and Cayley numbers algebra and applications by J. P. Ward, Department of Mathematical Sciences, Loughborough University, Loughborough, England Dordrecht [u.a.] Kluwer Academic Publishers 1997 XI, 237 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and Its Applications 403 Cayley numbers Quaternions Mathematics and Its Applications 403 (DE-604)BV008163334 403 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007814646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ward, Joseph P. 1949- Quaternions and Cayley numbers algebra and applications Mathematics and Its Applications Cayley numbers Quaternions |
| title | Quaternions and Cayley numbers algebra and applications |
| title_auth | Quaternions and Cayley numbers algebra and applications |
| title_exact_search | Quaternions and Cayley numbers algebra and applications |
| title_full | Quaternions and Cayley numbers algebra and applications by J. P. Ward, Department of Mathematical Sciences, Loughborough University, Loughborough, England |
| title_fullStr | Quaternions and Cayley numbers algebra and applications by J. P. Ward, Department of Mathematical Sciences, Loughborough University, Loughborough, England |
| title_full_unstemmed | Quaternions and Cayley numbers algebra and applications by J. P. Ward, Department of Mathematical Sciences, Loughborough University, Loughborough, England |
| title_short | Quaternions and Cayley numbers |
| title_sort | quaternions and cayley numbers algebra and applications |
| title_sub | algebra and applications |
| topic | Cayley numbers Quaternions |
| topic_facet | Cayley numbers Quaternions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007814646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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