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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010029175 | QA76.9 M35 A658 2002 | Open Access Book | Book | Searching... |
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Summary
Summary
Geometric algebra has established itself as a powerful and valuablemathematical tool for solving problems in computer science,engineering, physics, and mathematics. The articles in this volume,written by experts in various fields, reflect an interdisciplinaryapproach to the subject, and highlight a range of techniques andapplications. Relevant ideas are introduced in a self-contained mannerand only a knowledge of linear algebra and calculus is assumed.Features and Topics:* The mathematical foundations of geometric algebra are explored* Applications in computational geometry include models of reflectionand ray-tracing and a new and concise characterization of thecrystallographic groups* Applications in engineering include robotics, image geometry,control-pose estimation, inverse kinematics and dynamics, control andvisual navigation* Applications in physics include rigid-body dynamics, elasticity, andelectromagnetism* Chapters dedicated to quantum information theory dealing with multi-particle entanglement, MRI, and relativistic generalizationsPractitioners, professionals, and researchers working in computerscience, engineering, physics, and mathematics will find a wide rangeof useful applications in this state-of-the-art survey and referencebook. Additionally, advanced graduate students interested in geometricalgebra will find the most current applications and methods discussed.
Table of Contents
| Preface |
| Contributors |
| Part I Algebra and Geometry Point Groups and Space Groups in Geometric AlgebraD. Hestenes |
| The Inner Products of Geometric AlgebraL. Dorst |
| Unification of Grassmann's Progressive and Regressive Products using the Principle of DualityS. Blake |
| From Unoriented Subspaces to Blade OperatorsT.A. Bouma |
| Automated Theorem Proving in the Homogeneous Model with Clifford Bracket AlgebraH. Li |
| Rotations in n Dimensions as Spherical VectorsW.E. Baylis and S. Hadi |
| Geometric and Algebraic Canonical FormsN. Gordon |
| Functions of Clifford Numbers or Square MatricesJ. Snygg |
| Compound Matrices and Pfaffians: A Representation of Geometric AlgebraU. Prells and M.I. Friswell and S.D. Garvey |
| Analysis Using Abstract Vector VariablesF. Sommen |
| A Multivector Data Structure for Differential Forms and EquationsJ.A. Chard and V. Shapiro |
| Jet Bundles and the Formal Theory of Partial Differential EquationsR. Baker and C. Doran |
| Imaginary Eigenvalues and Complex Eigenvectors Explained by Real GeometryE.M.S. Hitzer |
| Symbolic Processing of Clifford Numbers in C++J.P. Fletcher |
| Clifford Numbers and their Inverses Calculated using the Matrix RepresentationJ.P. Fletcher |
| A Toy Vector Field Based on Geometric AlgebraA. Rockwood and S. Binderwala |
| Quadratic Transformations in the Projective PlaneG. Georgiev |
| Annihilators of Principal Ideals in the Grassmann AlgebraC. Koc/S. Esin |
| Part II Applications to Physics Homogeneous Rigid Body Mechanics with Elastic CouplingD. Hestenes and E.D. Fasse |
| Analysis of One and Two Particle Quantum Systems using Geometric AlgebraR. Parker and C. Doran |
| Interaction and Entanglement in the Multiparticle Spacetime AlgebraT.F. Havel and C.J.L. Doran |
| Laws of Reflection from Two or More Plane Mirrors in SuccessionM. Derome |
| Exact Kinetic Energy Operators for Polyatomic MoleculesJ. Pesonen |
| Geometry of Quantum Computing by Hamiltonian Dynamics of Spin EnsemblesT. Schulte-Herbruggen and K. Huper and U. Helmke and S.J. Glaser |
| Is the Brain a 'Clifford Algebra Quantum Computer'?V. Labunets and E. Rundblad and J. Astola |
| A Hestenes Spacetime Algebra Approach to Light PolarizationQ.M. Sugon and D. McNamara |
| Quaternions, Clifford Algebra and Symmetry GroupsP.R. Girard |
| Part III Computer Vision and Robotics A Generic Framework for Image GeometryJ.J. Koenderink |
| Color Edge Detection Using RotorsE. Bayro-Corrochano and S. Flores |
| Numerical Evaluation of Versors with Clifford AlgebraC.B.U. Perwass and G. Sommer |
| The Role of Clifford Algebra in Structure-Preserving Transformations for Second-Order SystemsS.D. Garvey and M.I. Friswell and U. Prells |
| Applications of Algebra of Incidence in Visually Guided RoboticsE. Bayro-Corrochano and P. Lounesto and L.R. Lozano |
| Monocular Pose Estimation of Kinematic ChainsB. Rosenhahn and O. Granert and G. Sommer |
| Stabilization of 3D Pose EstimationW. Neddermeyer and M. Schnell and W. Winkler and A. Lilienthal |
| Inferring Dynamical Information from 3D Position Data using Geometric AlgebraH. Udugama and G.S. Sajeewa and J. Lasenby |
| Clifford Algebra Space Singularities of Inline Planar PlatformsM.A. Baswell and R. Ablamowicz and J.N. Anderson |
| Part IV Signal Processing and Other Applications Fast Quantum Fourier--Heisenberg--Weyl TransformsV. Labunets and E. Rundblad and J. Astola |
| The Structure MultivectorM. Felsberg and G. Sommer |
| The Application of Clifford Algebra to Calculations of Multicomponent Chemical CompositionJ.P. Fletcher |
| An Algorithm to Solve the Inverse IFS-ProblemE. Hocevar |
| Fast Quantum n-D Fourier and Radon TransformsV. Labunets and E. Rundblad and J. Astola |
