Results 141 to 150 of about 245 (169)
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Clifford Algebra to Geometric Calculus
1984Geometric Calculus is a language for expressing and analyzing the full range of geometric concepts in mathematics. Clifford Algebra provides the grammar. Complex number, quaternions, matrix algebra, vector, tensor and spinor calculus and differential forms are integrated in to a single comprehensive system.
David Hestenes, Garret Sobczyk
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A Clifford Algebraic Method for Geometric Reasoning
1999In this paper a method for mechanical theorem proving in geometries is proposed. We first discuss how to describe geometric objects and geometric relations in 2D and/or 3D Euclidean space with Clifford algebraic expression. Then we present some rules to simplify Clifford algebraic polynomials to the so-called final Clifford algebraic polynomials.
Haiquan Yang +2 more
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Magnetic Order in Clifford Geometric Algebra
Journal of the Physical Society of Japan, 2006The observation of magnetic Bragg peaks, by both neutron and x-ray diffraction, which cannot be explained in terms of a single ordering wave vector has stimulated the suggestion of the coexistence of multiple magnetic-order-parameters. The peaks are empirically classified into distinct sets on the basis of their symmetry and relative intensities, and ...
Elizabeth Blackburn, Nic Bernhoeft
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Current survey of Clifford geometric algebra applications
Mathematical Methods in the Applied Sciences, 2022We extensively survey applications of Clifford Geometric algebra in recent years (mainly 2019–2022). This includes engineering; electric engineering; optical fibers; geographic information systems; geometry; molecular geometry; protein structure; neural networks; artificial intelligence; encryption; physics; signal, image, and video processing; and ...
Eckhard Hitzer +2 more
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Homomorphic Data Concealment Powered by Clifford Geometric Algebra
2020We propose general-purpose methods for data representation and data concealment via multivector decompositions and a small subset of functions in the three dimensional Clifford geometric algebra. We demonstrate mechanisms that can be explored for purposes from plain data manipulation to homomorphic data processing with multivectors. The wide variety of
David William Honorio Araujo da Silva +4 more
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Lectures on Clifford (Geometric) Algebras and Applications
2004Preface (Rafal Ablamowicz and Garret Sobczyk) * Lecture 1: Introduction to Clifford Algebras (Pertti Lounesto) * 1.1 Introduction * 1.2 Clifford algebra of the Euclidean plane * 1.3 Quaternions * 1.4 Clifford algebra of the Euclidean space R3 * 1.5 The electron spin in a magnetic field * 1.6 From column spinors to spinor operators * 1.7 In 4D: Clifford
Rafal Ablamowicz +7 more
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Symbolic computation in the homogeneous geometric model with clifford algebra
Proceedings of the 2004 international symposium on Symbolic and algebraic computation, 2004Clifford algebra provides nice algebraic representations for Euclidean geometry via the homogeneous model, and is suitable for doing geometric reasoning through symbolic computation. In this paper, we propose various symbolic computation techniques in Clifford algebra.
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Geometric Encoding of Sentences based on Clifford Algebra
2012Natural language sentences can be represented as vectors in a high dimensional vector space. Generally, these models are based on bag of words approaches, and therefore they do not fully capture the semantics of sentences which depends both by the semantics of the words, and their order in in the phrase.
Agnese Augello +3 more
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Remarks on invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebras
2001The invariant geometric calculus was founded by the German mathematician H.G. Grassmann in 1844 (Ausdehnungslehre [15, 16]). In this treatise, he introduced the modern notion of a vector in an abstract n-dimensional space and, in general, the notion of an extensor (decomposable antisymmetric tensor).
BRAVI, Paolo, A. BRINI
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