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Quaternions and Cayley Numbers : Algebra and Applications : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - J.P. Ward

Quaternions and Cayley Numbers : Algebra and Applications

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

By: J.P. Ward

Hardcover

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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.

Preface
Fundamentals of Linear Algebra
Quaternions
Complexified Quaternions
Cayley Numbers
Clifford Algebras
Computer Algebra and Cayley Numbers
References
Index
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345138
ISBN-10: 0792345134
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 242
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 2.54
Weight (kg): 0.61