Title | Applications of Geometric Algebra in Computer Science and Engineering [electronic resource] / edited by Leo Dorst, Chris Doran, Joan Lasenby |
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Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0089-5 |
Descript | XXV, 478 p. online resource |
1 Point Groups and Space Groups in Geometric Algebra -- 2 The Inner Products of Geometric Algebra -- 3 Unification of Grassmannโs Progressive and Regressive Products using the Principle of Duality -- 4 From Unoriented Subspaces to Blade Operators -- 5 Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra -- 6 Rotations in n Dimensions as Spherical Vectors -- 7 Geometric and Algebraic Canonical Forms -- 8 Functions of Clifford Numbers or Square Matrices -- 9 Compound Matrices and PfafRans: A Representation of Geometric Algebra -- 10 Analysis Using Abstract Vector Variables -- 11 A Multivector Data Structure for Differential Forms and Equations -- 12 Jet Bundles and the Formal Theory of Partial Differential Equations -- 13 Imaginary Eigenvalues and Complex Eigenvectors Explained by Real Geometry -- 14 Symbolic Processing of Clifford Numbers in C++ -- 15 Clifford Numbers and their Inverses Calculated using the Matrix Representation -- 16 A Toy Vector Field Based on Geometric Algebra -- 17 Quadratic Transformations in the Projective Plane -- 18 Annihilators of Principal Ideals in the Grassmann Algebra -- 19 Homogeneous Rigid Body Mechanics with Elastic Coupling -- 20 Analysis of One and Two Particle Quantum Systems using Geometric Algebra -- 21 Interaction and Entanglement in the Multiparticle Spacetime Algebra -- 22 Laws of Reflection from Two or More Plane Mirrors in Succession -- 23 Exact Kinetic Energy Operators for Polyatomic Molecules -- 24 Geometry of Quantum Computing by Hamiltonian Dynamics of Spin Ensembles -- 25 Is the Brain a โClifford Algebra Quantum Computerโ? -- 26 A Hestenes Spacetime Algebra Approach to Light Polarization -- 27 Quaternions, Clifford Algebra and Symmetry Groups -- 28 A Generic Framework for Image Geometry -- 29 Color Edge Detection Using Rotors -- 30 Numerical Evaluation of Versors with Clifford Algebra -- 31 The Role of Clifford Algebra in Structure-Preserving Transformations for Second-Order Systems -- 32 Applications of Algebra of Incidence in Visually Guided Robotics -- 33 Monocular Pose Estimation of Kinematic Chains -- 34 Stabilization of 3D Pose Estimation -- 35 Inferring Dynamical Information from 3D Position Data using Geometric Algebra -- 36 Clifford Algebra Space Singularities of Inline Planar Platforms -- 37 Fast Quantum FourierโHeisenbergโWeyl Transforms -- 38 The Structure Multivector -- 39 The Application of Clifford Algebra to Calculations of Multicomponent Chemical Composition -- 40 An Algorithm to Solve the Inverse IFS-Problem -- 41 Fast Quantum n-D Fourier and Radon Transforms