# Quaternions and Cayley Numbers

## Algebra and Applications

• J. P. Ward
Book

Part of the Mathematics and Its Applications book series (MAIA, volume 403)

1. Front Matter
Pages i-xi
2. J. P. Ward
Pages 1-53
3. J. P. Ward
Pages 54-104
4. J. P. Ward
Pages 105-163
5. J. P. Ward
Pages 164-216
6. Back Matter
Pages 217-242

### Introduction

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 - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e.

### Keywords

Matrix algebra associative algebra computer algebra linear algebra non-associative algebra

#### Authors and affiliations

• J. P. Ward
• 1
1. 1.Department of Mathematical SciencesLoughborough UniversityLoughboroughEngland

### Bibliographic information

• DOI https://doi.org/10.1007/978-94-011-5768-1