Geometric Algebra with Applications in Science and Engineering

1. Quantum and Neural Computing, and Wavelets

   1. Geometric Feedforward Neural Networks and Support Multivector Machines

      • Eduardo Bayro Corrochano, Refugio Vallejo

      Pages 309-325

   2. Image Analysis Using Quaternion Wavelets

      • Leonardo Traversoni

      Pages 326-345

2. Applications to Engineering and Physics

   1. Front Matter

      Pages 347-347

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   2. Objects in Contact: Boundary Collisions as Geometric Wave Propagation

      • Leo Dorst

      Pages 349-370

   3. Modern Geometric Calculations in Crystallography

      • G. Aragon, J. L. Aragon, F. Davila, A. Gomez, M. A. Rodriguez

      Pages 371-386

   4. Quaternion Optimization Problems in Engineering

      • Ljudmila Meister

      Pages 387-412

   5. Clifford Algebras in Electrical Engineering

      • William E. Baylis

      Pages 413-429

   6. Applications of Geometric Algebra in Physics and Links With Engineering

      • Anthony Lasenby, Joan Lasenby

      Pages 430-457

3. Computational Methods in Clifford Algebras

   1. Front Matter

      Pages 459-459

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   2. Clifford Algebras as Projections of Group Algebras

      • Vladimir M. Chernov

      Pages 461-476

   3. Counterexamples for Validation and Discovering of New Theorems

      • Pertti Lounesto

      Pages 477-490

   4. The Making of GABLE: A Geometric Algebra Learning Environment in Matlab

      • Stephen Mann, Leo Dorst, Tim Bouma

      Pages 491-511

   5. Helmstetter Formula and Rigid Motions with CLIFFORD

      • Rafal Ablamowicz

      Pages 512-534

4. Back Matter

   Pages 535-592

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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.

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

• Centro de Investigación y de Estudios Avanzados, CINVESTAV, Guadalajara, Mexico

  Eduardo Bayro Corrochano

• Departamento de Fisica y Matematica, Universidad de las Americas-Puebla, Cholula, Mexico

  Garret Sobczyk

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