Computational Noncommutative Algebra and Applications
- Dedication. Preface. Acknowledgments
- Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries
- Content-Based Information Retrieval by Group Theoretical Methods
- Four Problems in Radar
- Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups
- Lie Groups and Lie Algebras in Robotics
- Quantum/Classical Interface: a Geometric Approach from the Classical Side
- PONS, Reed-Muller Codes, and Group Algebras
- Clifford Algebras as a Unified Language
- Recent Progress and Applications in Group FFTs
- Group Filters and Image Processing
- A Geometric Algebra Approach to Some Problems of Robot Vision
- Group Theory in Radar and Signal Processing
- Geometry of Paravector Space with Applications to Relativistic Physics
- A Unified Approach to Fourier-Clifford-Prometheus Transforms
- Fast Color Wavelet Transforms
- Selected Problems
- Topic Index
- Author Index
Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries;Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction-Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti);Shapiro Sequences, Reed-Muller Codes, and Functional Equations;Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; Group Algebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces;Hypercomplex-Valued invariants of nD
- 2005, XVI, 427 Seiten, Maße: 16,2 x 24,2 cm, Kartoniert (TB), Englisch
- Herausgegeben: J. Byrnes, G. Ostheimer
- Verlag: Springer Netherland
- ISBN-10: 1402019831
- ISBN-13: 9781402019838
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