Quaternions and Cayley Numbers Algebra and Applications

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

In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - g...

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Bibliographic Details
Main Author: Ward, J.P (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 1997.
Edition:1st ed. 1997.
Series:Mathematics and Its Applications ; 403
Springer eBook Collection.
Subjects:
Associative rings.
Rings (Algebra).
Nonassociative rings.
Matrix theory.
Algebra.
Mathematical physics.
Applied mathematics.
Engineering mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Fundamentals of Linear Algebra
  • 1.1 Integers, Rationals and Real Numbers
  • 1.2 Real Numbers and Displacements
  • 1.3 Groups
  • 1.4 Rings and Fields
  • 1.5 Linear Spaces
  • 1.6 Inner Product Spaces
  • 1.7 Algebras
  • 1.8 Complex Numbers
  • 2 Quaternions
  • 2.1 Inventing Quaternions
  • 2.2 Quaternion Algebra
  • 2.3 The Exponential Form and Root Extraction
  • 2.4 Frobenius’ Theorem
  • 2.5 Inner Product for Quaternions
  • 2.6 Quaternions and Rotations in 3- and 4-Dimensions
  • 2.7 Relation to the Rotation Matrix
  • 2.8 Matrix Formulation of Quaternions
  • 2.9 Applications to Spherical Trigonometry
  • 2.10 Rotating Axes in Mechanics
  • 3 Complexified Quaternions
  • 3.1 Scalars, Pseudoscalars, Vectors and Pseudovectors
  • 3.2 Complexified Quaternions: Euclidean Metric
  • 3.3 Complexified Quaternions: Minkowski Metric
  • 3.4 Application of Complexified Quaternions to Space-Time
  • 3.5 Quaternions and Electromagnet ism
  • 3.6 Quaternionic Representation of Bivectors
  • 3.7 Null Tetrad for Space-time
  • 3.8 Classification of Complex Bivectors and of the Weyl Tensor
  • 4 Cayley Numbers
  • 4.1 A Common Notation for Numbers
  • 4.2 Cayley Numbers
  • 4.3 Angles and Cayley Numbers
  • 4.4 Cayley Number Identities
  • 4.5 Normed Algebras and the Hurwitz Theorem
  • 4.6 Rotations in 7-and 8-Dimensional Euclidean Space
  • 4.7 Basis Elements for Cayley Numbers
  • 4.8 Geometry of 8-Dimensional Rotations
  • Appendix 1 Clifford Algebras
  • Appendix 2 Computer Algebra and Cayley Numbers
  • References.

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