Clifford Algebra to Geometric Calculus

Clifford Algebra to Geometric Calculus
Author : D. Hestenes
Publisher : Springer Science & Business Media
Total Pages : 314
Release : 2012-12-06
ISBN 10 : 9789400962927
ISBN 13 : 9400962924
Language : EN, FR, DE, ES & NL

Clifford Algebra to Geometric Calculus Book Description:

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 Algebm' 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 quatemions, 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.


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A New Approach to Differential Geometry using Clifford's Geometric Algebra
Language: en
Pages: 465
Authors: John Snygg
Categories: Mathematics
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Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for