Applications of Clifford's Geometric Algebra

Abstract

We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond.

26 pages, 91 references

References in corpus (4)

• Quaternion Fourier Transform on Quaternion Fields and Generalizations
• Introduction to Clifford's Geometric Algebra
• Biquaternion (complexified quaternion) roots of -1
• OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions

Cited by in corpus (10)

• Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space
• A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
• Hypercomplex-Valued Recurrent Correlation Neural Networks
• Further investigation of mass dimension one fermionic duals
• Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks
• On generalization of Lipschitz groups and spin groups
• Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks
• Symbolic and User-friendly Geometric Algebra Routines (SUGAR) for Computations in Matlab
• Novel computational workflows for natural and biomedical image processing based on hypercomplex algebras
• Two-sided Clifford Fourier transform with two square roots of -1 in Cl(p,q)