Geometric Algebra in Linear Algebra and Geometry

Acta Applicandae Mathematicae - Tập 71 - Trang 207-244 - 2002
José María Pozo1, Garret Sobczyk2
1Departament de Física Fonamental, Universitat de Barcelona, Barcelona, Spain
2Departamento de Fisica y Matematicas, Universidad de las Américas-Puebla, Cholula, México, Mexico

Tóm tắt

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 tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.

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Acta Applicandae Mathematicae

Tập 71

207-244

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