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Geometric Algebra with Applications in Science and Engineering

  • Eduardo Bayro Corrochano
  • Garret Sobczyk

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Advances in Geometric Algebra

    1. Front Matter
      Pages 1-1
    2. Garret Sobczyk
      Pages 18-41
    3. Jose Maria Pozo, Garret Sobczyk
      Pages 42-60
    4. Hongbo Li
      Pages 61-85
  3. Theorem Proving

    1. Front Matter
      Pages 87-87
    2. Dongming Wang
      Pages 89-109
    3. Hongbo Li
      Pages 110-119
  4. Computer Vision

    1. Front Matter
      Pages 121-121
    2. Eduardo Bayro Corrochano, Joan Lasenby
      Pages 123-146
    3. Joan Lasenby, Adam Stevenson
      Pages 147-169
    4. Eduardo Bayro Corrochano, Vladimir Banarer
      Pages 190-208
  5. Robotics

    1. Front Matter
      Pages 209-209
    2. J. M. Selig
      Pages 211-234
    3. Shawn G. Ahlers, John Michael McCarthy
      Pages 235-251
    4. Eduardo Bayro Corrochano, Garret Sobczyk
      Pages 252-277
  6. Quantum and Neural Computing, and Wavelets

    1. Front Matter
      Pages 279-279
    2. Timothy F. Havel, David G. Cory, Shyamal S. Somaroo, Ching-Hua Tseng
      Pages 281-308
    3. Eduardo Bayro Corrochano, Refugio Vallejo
      Pages 309-325
    4. Leonardo Traversoni
      Pages 326-345
  7. Applications to Engineering and Physics

    1. Front Matter
      Pages 347-347
    2. G. Aragon, J. L. Aragon, F. Davila, A. Gomez, M. A. Rodriguez
      Pages 371-386
    3. Ljudmila Meister
      Pages 387-412
    4. William E. Baylis
      Pages 413-429
  8. Computational Methods in Clifford Algebras

    1. Front Matter
      Pages 459-459
    2. Vladimir M. Chernov
      Pages 461-476
    3. Stephen Mann, Leo Dorst, Tim Bouma
      Pages 491-511
  9. Back Matter
    Pages 535-592

About this book

Introduction

The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer­ ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar­ ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math­ ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop­ ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.

Keywords

Algebra Applied Math Engineering Physics Potential Signal computer science computer vision filtering image processing mathematics optimization robot robotics

Editors and affiliations

  • Eduardo Bayro Corrochano
    • 1
  • Garret Sobczyk
    • 2
  1. 1.Centro de Investigación y de Estudios AvanzadosCINVESTAVGuadalajaraMexico
  2. 2.Departamento de Fisica y MatematicaUniversidad de las Americas-PueblaCholulaMexico

Bibliographic information