Gourt > Science > Math > Algebra > Geometric Algebra (1)
Geometric algebra is a form of mathematics and a species of multilinear algebra, namely a Clifford algebra with a geometric interpretation. Geometric algebras are a fruitful way of formalizing substantial parts of theoretical physics, especially those parts involving one or more of rotations, phases, and complex numbers. Advocates of geometric algebra submit that it describes classical mechanics, quantum mechanics, electromagnetic theory, and relativity more compactly and intuitively than do standard methods. Geometric algebra has also been applied to engineering problems such as computer vision, biomechanics and robotics, and the dynamics of space flight.
The geometric product
A geometric algebra is an algebra constructed over a vector space in which a geometric product is defined. The elements of geometric algebra are multivectors. The geometric product has the following properties, for all multivectors :
- Closure
- Distributivity over the addition of multivectors:
- Associativity
- Unit (scalar) element:
- Tensor contraction: for any "vector" (a grade-one element) is a scalar (real number)
- Commutativity of the product by a scalar:
Mathematical Physics :: Physics
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Advances in Applied Clifford Algebras - This journal publishes research papers and notes, expository and survey articles, book reviews, reproduces abstracts and also reports on conferences and workshops in the area of Clifford Algebras and their applications to other branches of mathematics and physics, and in certain cognate areas.
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Advances in Applied Clifford Algebras - Electronic version of the journal published by the Universidad Nacional Autónoma de México. Publishes original research papers, expository and survery articles, book reviews, reproduces abstracts and reports on conferences and workshops in the area of Clifford Algebras and their applications.
Clifford - A Maple package for computations in Clifford algebras of an arbitrary bilinear form. Includes documentations of new features and installation information, as well as downloads of the software.
Meta Description: [ CLIFFORD (ver. 5) with 'Bigebra' is a Maple V Rel. 5 package for computations in Clifford algebras of an arbitrary bilinear form ]
GA-Net - Free electronic newsletter on Clifford algebra and geometric algebra. Archive, free subscription functions and submission information.
Meta Description: [ Geometric Algebra, Clifford Algebra, Newsletter, GA-Net ]
Geometric Algebra and its Applications in Mathematical Physics - C.J.L. Doran's thesis on applications of Clifford algebras. Downloadable in PostScript format.
Geometric Calculus Research and Development - Includes a brief introduction, articles and book chapters on the subject, as well as references to further information.
ICCA7 - 7th International conference on Clifford Analysis and their applications in Mathematical Physics. Université Paul Sabatier, Toulouse, France; 19--29 May 2005.
International Clifford Algebra Society - Includes an abstracts mailing list, information on events and back copies of the journal Advances in Applied Clifford Algebras
Maths for (Games) Programmers: Multivector Methods - An introduction on this formalism and its applications in space-time.
Meta Description: [ maths\geoalg.htm contents page ]
The CLU Project - Aims to produce tools for use with Clifford algebra. Includes information on the visualisation libraries and calculators produced, as well as downloads.
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