Applications of Geometric Algebra in Computer Science and Engineering

Preface
Contributors
I. Algebra and Geometry
1. Point Groups and Space Groups in Geometric Algebra (D. Hestenes)
2. The Inner Products of Geometric Algebra (L. Dorst)
3. Unification of Grassmann's Progressive and Regressive Products using the Principle of Duality (S. Blake)
4. From Unoriented Subspaces to Blade Operators (T.A. Bouma)
5. Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra (H. Li)
6. Rotations in n Dimensions as Spherical Vectors (W.E. Baylis/S. Hadi)
7. Geometric and Algebraic Canonical Forms (N. Gordon)
8. Function of Clifford Numbers or Square Matrices (J. Snygg)
9. Compound Matrices and Pfaffians: A Representation of Geometric Algebra (U. Prells/M.I. Friswell/S.D. Garvey)
10. Analysis Using Abstract Vector Variables (F. Sommen)
11. A Multivector Data Structure for Differential Forms and Equations (J.A. Chard/V. Shapiro)
12. Jet Bundles and the Formal Theory of Partial Differential Equations (R. Baker/C. Doran)
13. Imaginary Eigenvalues and Complex Eigenvectors Explained by Real Geometry (E.M.S. Hitzer)
14. Symbolic Processing of Clifford Numbers in C++ (J.P. Fletcher)
15. Clifford Numbers and Their Inverses Calculated using the Matrix Representation (J.P. Fletcher)
16. A Toy Vector Field Based on Geometric Algebra (A. Rockwood/S. Binderwala)
17. Quadratic Transformations in the Projective Plane (G. Georgiev)
18. Annihilators of Principal Ideals in the Grassmann Algebra (C. Koc/S. Esin)
19. Homogeneous Rigid Body Mechanics with Elastic Coupling (D. Hestenes/E.D. Fasse)
20. Analysis of 1 and 2 Particle Quantum Systems using Geometric Algebra (R. Parker/C. Doran)
21. Interaction and Entanglement in the Multiparticle Space-time Algebra (T.F. Havel/C.J.L. Doran)
22. Laws of Reflection from Two or More Plane Mirrors in Succession (M. Derome)
23. Exact Kinetic Energy Operators for Polyatomic Molecules (J. Pesonen)
24. Geometry of Quantum Computing by Hamiltonian Dynamics of...

"This book contains papers presented at the conference "Applied Geometric Algebra in Computer Science and Engineering" (AGACSE 2001)!. The goal was to demonstrate how the framework of geometric algebra (Clifford algebra) could unify and illuminate diverse fields of science and engineering. The articles reveal [a] range [of] fields: from quantum physics to robotics, from crystallographic groups to image understanding, from relativistic mechanics to signal processing. Despite this diversity, the combination of these subjects was not felt to be artificial. This book should be!useful to mathematicians!physicists, [and] to mechanical and computer engineers." --Iasi Polytechnic Magazine "The conference 'Applied Geometric Algebras in Computer Science and Engineering' (AGACSE 2001) was held! July 9--13, 2001. The present book contains the papers of this scientific meeting and reflects the constantly growing interest in searching the applications of geometric algebra (or Clifford algebra) in various fields of science. Geometric algebra includes a lot of techniques from several mathematical theories (linear algebra, vector calculus, projective geometry, complex analysis) and offers new directions in some unexpected domains like quantum physics, robotics, crystallographic groups, image understanding, relativistic mechanics, signal processing. The volume begins with a preface written by the Editors and a useful list with contributors!. There are four sections: Algebra and Geometry!, Applications to Physics!, Computer Vision and Robotics!, Signal Processing and Other Applications!. In conclusion, a very useful book both for beginners and specialists!" --Memoriile Sectiilor Stiintifice