Clifford (Geometric) Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 1461241049
Total Pages : 522 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Clifford (Geometric) Algebras by : William E. Baylis

Download or read book Clifford (Geometric) Algebras written by William E. Baylis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.

Clifford (Geometric) Algebras

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Publisher :
ISBN 13 : 9781461241058
Total Pages : 540 pages
Book Rating : 4.2/5 (41 download)

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Book Synopsis Clifford (Geometric) Algebras by : William E Baylis

Download or read book Clifford (Geometric) Algebras written by William E Baylis and published by . This book was released on 1996-08-01 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering

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Author :
Publisher : Boston : Birkhäuser
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering by : William Eric Baylis

Download or read book Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering written by William Eric Baylis and published by Boston : Birkhäuser. This book was released on 1996 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a comprehensive approach to the theoretical, applied and symbolic computational aspects of the subject. Excellent for self-study, leading experts in the field have written on the of topics mentioned above, using an easy approach with efficient geometric language for non-specialists.

Clifford Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 1461220440
Total Pages : 635 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Clifford Algebras by : Rafal Ablamowicz

Download or read book Clifford Algebras written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

Geometric Algebra with Applications in Engineering

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Publisher : Springer Science & Business Media
ISBN 13 : 3540890688
Total Pages : 389 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Geometric Algebra with Applications in Engineering by : Christian Perwass

Download or read book Geometric Algebra with Applications in Engineering written by Christian Perwass and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation. Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.

Lectures on Clifford (Geometric) Algebras and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 0817681906
Total Pages : 221 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Lectures on Clifford (Geometric) Algebras and Applications by : Rafal Ablamowicz

Download or read book Lectures on Clifford (Geometric) Algebras and Applications written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.

Clifford Algebra to Geometric Calculus

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Publisher : Springer Science & Business Media
ISBN 13 : 9789027725615
Total Pages : 340 pages
Book Rating : 4.7/5 (256 download)

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Book Synopsis Clifford Algebra to Geometric Calculus by : David Hestenes

Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer Science & Business Media. This book was released on 1984 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.

Geometric Algebra with Applications in Science and Engineering

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Publisher : Springer Science & Business Media
ISBN 13 : 9780817641993
Total Pages : 632 pages
Book Rating : 4.6/5 (419 download)

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Book Synopsis Geometric Algebra with Applications in Science and Engineering by : Eduardo Bayro Corrochano

Download or read book Geometric Algebra with Applications in Science and Engineering written by Eduardo Bayro Corrochano and published by Springer Science & Business Media. This book was released on 2001-04-20 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.

Clifford Algebras and their Applications in Mathematical Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 9401580901
Total Pages : 509 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Clifford Algebras and their Applications in Mathematical Physics by : A. Micali

Download or read book Clifford Algebras and their Applications in Mathematical Physics written by A. Micali and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers presented at the Second Workshop on Clifford Algebras and their Applications in Mathematical Physics. These papers range from various algebraic and analytic aspects of Clifford algebras to applications in, for example, gauge fields, relativity theory, supersymmetry and supergravity, and condensed phase physics. Included is a biography and list of publications of Mário Schenberg, who, next to Marcel Riesz, has made valuable contributions to these topics. This volume will be of interest to mathematicians working in the fields of algebra, geometry or special functions, to physicists working on quantum mechanics or supersymmetry, and to historians of mathematical physics.

Applications of Geometric Algebra in Computer Science and Engineering

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Publisher : Springer Science & Business Media
ISBN 13 : 146120089X
Total Pages : 479 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Applications of Geometric Algebra in Computer Science and Engineering by : Leo Dorst

Download or read book Applications of Geometric Algebra in Computer Science and Engineering written by Leo Dorst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Clifford Algebras and their Applications in Mathematical Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 9780817641825
Total Pages : 500 pages
Book Rating : 4.6/5 (418 download)

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Book Synopsis Clifford Algebras and their Applications in Mathematical Physics by : Rafał Abłamowicz

Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafał Abłamowicz and published by Springer Science & Business Media. This book was released on 2000 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.

Clifford Algebras

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Publisher : Birkhäuser
ISBN 13 : 9781461273936
Total Pages : 626 pages
Book Rating : 4.2/5 (739 download)

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Book Synopsis Clifford Algebras by : Rafal Ablamowicz

Download or read book Clifford Algebras written by Rafal Ablamowicz and published by Birkhäuser. This book was released on 2011-09-30 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

Clifford Algebra in Mathematics and Physics

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Author :
Publisher : Arcler Press
ISBN 13 : 9781773611266
Total Pages : 0 pages
Book Rating : 4.6/5 (112 download)

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Book Synopsis Clifford Algebra in Mathematics and Physics by : Stefano Spezia

Download or read book Clifford Algebra in Mathematics and Physics written by Stefano Spezia and published by Arcler Press. This book was released on 2017-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Clifford or geometric algebra (GA) is an algebra generated by a vector space with a bilinear form with some special properties. GA is more efficient than the matrix algebra because of the fact that the components of geometric algebra can be expressed without introducing any arbitrary basis and turned out to be a superior mathematical tool which provides a common mathematical language that aids a unified approach and understanding in topics across mathematics, physics and engineering. For example, complex variables, vectors, quaternions, matrix theory, differential forms, tensor calculus, spinors and twistors, are all subsumed under a common approach.The book begins with a brief historical introduction, followed by a description of the mathematical formalism of Clifford algebra. In particular, definitions, axiom and examples applied to two-dimensional and three-dimensional spaces have been presented. Section 1 gives an overview of the application of GA in Physics, focusing on geometric algebra pictures of both the plane wave solution of the Maxwell equation and special relativity, a toy model of SU(3) symmetry, and some preliminary thoughts about a possible geometric meaning of quantum mechanics. In particular, it is cleared that the internal spin structure of the particle is hidden in both Schrödinger and Dirac equations showing that the classical mechanics combined with zero-point field leads to quantum mechanics. Section 2 discusses the problem of quantization in quantum theory, a natural algebraic alternative definition of time, a coordinate-free formulation of General Relativity, a more unified and systematic description of flux compactifications and of supergravity and string compactifications in general. Finally, the last Section 3 begins with the study of the association of a quaternion algebra to the set of generalized Fibonacci quaternions by using the construction of Clifford algebras and concludes with the study of an important branch of modern analysis: The Clifford analysis.

Geometric Algebra with Applications in Science and Engineering

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461201594
Total Pages : 592 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometric Algebra with Applications in Science and Engineering by : Eduardo Bayro Corrochano

Download or read book Geometric Algebra with Applications in Science and Engineering written by Eduardo Bayro Corrochano and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.

Quaternions, Clifford Algebras and Relativistic Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 3764377917
Total Pages : 180 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Quaternions, Clifford Algebras and Relativistic Physics by : Patrick R. Girard

Download or read book Quaternions, Clifford Algebras and Relativistic Physics written by Patrick R. Girard and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism, and general relativity.

Clifford Algebras and their Applications in Mathematical Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 1461213681
Total Pages : 470 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Clifford Algebras and their Applications in Mathematical Physics by : Rafal Ablamowicz

Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.

Geometric Algebra for Physicists

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Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521480222
Total Pages : 596 pages
Book Rating : 4.4/5 (82 download)

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Book Synopsis Geometric Algebra for Physicists by : Chris Doran

Download or read book Geometric Algebra for Physicists written by Chris Doran and published by Cambridge University Press. This book was released on 2003-05-29 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering.