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Quaternions and Cayley Numbers

Algebra and Applications

  • Book
  • © 1997

Overview

Authors:
  1. J. P. Ward

    1. Department of Mathematical Sciences, Loughborough University, Loughborough, England

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xi
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  2. Fundamentals of Linear Algebra

    • J. P. Ward
    Pages 1-53

  3. Quaternions

    • J. P. Ward
    Pages 54-104

  4. Complexified Quaternions

    • J. P. Ward
    Pages 105-163

  5. Cayley Numbers

    • J. P. Ward
    Pages 164-216

  6. Back Matter

    Pages 217-242
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematical Sciences, Loughborough University, Loughborough, England

    J. P. Ward

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