# Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics

@inproceedings{Hestenes1984CliffordAT,
title={Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics},
author={David Hestenes and Garret Sobczyk and James S. Marsh},
year={1984}
}
• Published 30 June 1984
• Mathematics
1 / Geometric Algebra.- 1-1. Axioms, Definitions and Identities.- 1-2. Vector Spaces, Pseudoscalars and Projections.- 1-3. Frames and Matrices.- 1-4. Alternating Forms and Determinants.- 1-5. Geometric Algebras of PseudoEuclidean Spaces.- 2 / Differentiation.- 2-1. Differentiation by Vectors.- 2-2. Multivector Derivative, Differential and Adjoints.- 2-3. Factorization and Simplicial Derivatives.- 3 / Linear and Multilinear Functions.- 3-1. Linear Transformations and Outermorphisms.- 3-2…
515 Citations
New Foundations in Mathematics: The Geometric Concept of Number
1 Modular Number Systems.- 2 Complex and Hyperbolic Numbers.- 3 Geometric Algebra.- 4 Vector Spaces and Matrices.- 5 Outer Product and Determinants.- 6 Systems of Linear Equations.- 7 Linear
Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries
Given a quadratic form on a vector space, the geometric algebra of the corresponding pseudo-euclidean space is defined in terms of a simple set of rules which characterizes the geometric product of
Geometric Manifolds Part I: The Directional Derivative of Scalar, Vector, Multivector, and Tensor Fields
This is the first entry in a planned series aiming to establish a modified, and simpler, formalism for studying the geometry of smooth manifolds with a metric, while remaining close to standard
Remarks on invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebras
• Mathematics
• 2001
The 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
Group Manifolds in Geometric Algebra Garret Sobczyk
This article explores group manifolds which are efficiently expressed in lower dimensional (Clifford) geometric algebras. The spectral basis of a geometric algebra allows the insightful transition
A covariant approach to geometry using geometric algebra
• Mathematics, Computer Science
• 2004
Using the mathematical framework of conformal geometric algebra – a 5-dimensional representation of 3-dimensional space – is shown to provide an elegant covariant approach to geometry, thus enabling us to deal simply with the projective and non-Euclidean cases.
Geometric Algebra in Linear Algebra and Geometry
• Mathematics
• 2002
This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic
NULL POLARITIES AS GENERATORS OF THE PROJECTIVE GROUP
It is well-known that the group of regular projective transf ormations of P 3 (R) is iso- morphic to the group of projective automorphisms of Klein's quadric M 4 2 ⊂ P 5 (R). We introduce the
Clifford Algebra, Lorentz Transformation and Unified Field Theory
According to a framework based on Clifford algebra $$C\ell (1,3)$$Cℓ(1,3), this paper gives a classification for elementary fields, and then derives their dynamical equations and transformation laws
Geometric Algebra and Particle Dynamics
Abstract.In a recent publication [1] it was shown how the geometric algebra G4,1, the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null