Quaternions and Cayley Numbers: Algebra and Applications J.P. Ward

ISBN: 9780792345138

Published: April 30th 1997

Hardcover

242 pages


Description

Quaternions and Cayley Numbers: Algebra and Applications  by  J.P. Ward

Quaternions and Cayley Numbers: Algebra and Applications by J.P. Ward
April 30th 1997 | Hardcover | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 242 pages | ISBN: 9780792345138 | 8.77 Mb

This monograph is an accessible account of the normed algebras over the real field, particularly the quaternions and the Cayley numbers. The application of quaternions to spherical geometry and to mechanics is considered and the relation betweenMoreThis monograph is an accessible account of the normed algebras over the real field, particularly the quaternions and the Cayley numbers.

The application of quaternions to spherical geometry and to mechanics is considered and the relation between quaternions and rotations in 3- and 4-dimensional Euclidean space is fully developed. The algebra of complexified quaternions is described and applied to electromagnetism and to special relativity. By looking at a 3-dimensional complex space we explore the use of a quaternion formalism to the Lorentz transformation and we examine the classification of electromagnetic and Weyl tensors.

In the final chapter, extensions of quaternion algebra to the alternative non-associative algebra of Cayley numbers are investigated. The standard Cayley number identities are derived and their use in the analysis of 7- and 8-dimensional rotations is studied. Appendices on Clifford algebras and on the use of dynamic computation in Cayley algebra are included.

Audience: This volume has been written at a level suitable for final year and postgraduate students.



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