Quaternions and Cayley Numbers
Subtitle: Algebra and Applications
By: by J. P. Ward
Series: Mathematics and Its Applications -- 403; Mathematics and Its Applications -- 403
Publisher: Springer Netherlands
Published: 1997
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 242
ISBN-13: 9789401064347; 9789401157681
Subjects: Mathematics; Algebra; Matrix theory
Description: 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 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.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.