Geometric Algebra with Applications in Science and Engineering
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Geometric Algebra with Applications in Science and Engineering

Geometric Algebra with Applications in Science and Engineering


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About the Book

All of the efforts to build an intelligent machine have not yet produced a satisfactory autonomous system, despite the great progress that has been made in developing computer hardware over the last three decades. The complexity of the tasks that a cognitive system must perform is still not understood well enough. Recent progress in signal theory, computer vision and robotics shows that they are somehow separated from each other. The use of linear algebra over the real and complex numbers has not been adequate for the modeling of higher order geometric objects such as lines, planes and volumes. The aim of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science and engineering using geometric algebra.

Table of Contents:
I Advances in Geometric Algebra.- 1 Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry.- 2 Universal Geometric Algebra.- 3 Realizations of the Conformal Group.- 4 Hyperbolic Geometry.- II Theorem Proving.- 5 Geometric Reasoning With Geometric Algebra.- 6 Automated Theorem Proving.- III Computer Vision.- 7 The Geometry Algebra of Computer Vision.- 8 Using Geometric Algebra for Optical Motion Capture.- 9 Bayesian Inference and Geometric Algebra: An Application to Camera Localization.- 10 Projective Reconstruction of Shape and Motion Using Invariant Theory.- IV Robotics.- 11 Robot Kinematics and Flags.- 12 The Clifford Algebra and the Optimization of Robot Design.- 13 Applications of Lie Algebras and the Algebra of Incidence.- V Quantum and Neural Computing, and Wavelets.- 14 Geometric Algebra in Quantum Information Processing by Nuclear Magnetic Resonance.- 15 Geometric Feedforward Neural Networks and Support Mul- tivector Machines.- 16 Image Analysis Using Quaternion Wavelets.- VI Applications to Engineering and Physics.- 17 Objects in Contact: Boundary Collisions as Geometric Wave Propagation.- 18 Modern Geometric Calculations in Crystallography.- 19 Quaternion Optimization Problems in Engineering.- 20 Clifford Algebras in Electrical Engineering.- 21 Applications of Geometric Algebra in Physics and Links With Engineering.- VII Computational Methods in Clifford Algebras.- 22 Clifford Algebras as Projections of Group Algebras.- 23 Counterexamples for Validation and Discovering of New Theorems.- 24 The Making of GABLE: A Geometric Algebra Learning Environment in Matlab.- 25 Helmstetter Formula and Rigid Motions with CLIFFORD.- References.


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Product Details
  • ISBN-13: 9780817641993
  • Publisher: Birkhauser Boston Inc
  • Publisher Imprint: Birkhauser Boston Inc
  • Height: 235 mm
  • No of Pages: 592
  • Returnable: Y
  • ISBN-10: 0817641998
  • Publisher Date: 20 Apr 2001
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Width: 155 mm


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