Results 141 to 150 of about 251 (170)
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Clifford, or Geometric, Algebra
2016AbstractIn this chapter, the so-called geometric algebras, or Clifford algebras, are introduced, with special attention to the universal Clifford algebras. As well as providing the standard definition of a Clifford algebra via the so-called Clifford mapping, this chapter presents an explicit construction of the universal Clifford algebra associated ...
Jayme Vaz, Roldão da Rocha
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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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Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl3,0
Advances in Applied Clifford Algebras, 2006First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions \( (f:\user2{\mathbb{R}}^3 \to Cl_{3,0} ).
Eckhard Hitzer
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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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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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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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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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Clifford algebraic calculus for geometric reasoning
1998In this paper we report on our recent study of Clifford algebra for geometric reasoning and its application to problems in computer vision. A general framework is presented for construction and representation of geometric objects with selected rewrite rules for simplification. It provides a mechanism suitable for devising methods and software tools for
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