Applications of Geometric Algebra in Computer Science and Engineering

1 Point Groups and Space Groups in Geometric Algebra.- 2 The Inner Products of Geometric Algebra.- 3 Unification of Grassmann’s 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 ‘Clifford Algebra Quantum Computer’?.- 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 DetectionUsing 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 Fourier—Heisenberg—Weyl 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.