Dewey Class 
519 
Title 
Applications of Geometric Algebra in Computer Science and Engineering ([EBook] /) / edited by Leo Dorst, Chris Doran, Joan Lasenby. 
Added Personal Name 
Dorst, Leo editor. 
Doran, Chris editor. 
Lasenby, Joan editor. 
Other name(s) 
SpringerLink (Online service) 
Publication 
Boston, MA : : Birkhäuser Boston : : Imprint: Birkhäuser, , 2002. 
Physical Details 
XXV, 478 p. : online resource. 
ISBN 
9781461200895 
Summary Note 
Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a selfcontained manner and 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 reflection and raytracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, controlpose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigidbody dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this stateoftheart survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.: 
Contents note 
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 Detection Using Rotors  30 Numerical Evaluation of Versors with Clifford Algebra  31 The Role of Clifford Algebra in StructurePreserving Transformations for SecondOrder 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 IFSProblem  41 Fast Quantum nD Fourier and Radon Transforms. 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9781461200895 
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