# Clifford Geometric Algebras in Multilinear Algebra and Non-euclidean Geometries

@inproceedings{SobczykCliffordGA, title={Clifford Geometric Algebras in Multilinear Algebra and Non-euclidean Geometries}, author={Garret Sobczyk} }

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 vectors. We develop geometric algebra in such a way that it augments, but remains fully compatible with, the more traditional tools of matrix algebra. Indeed, matrix multiplication arises naturally from the geometric multiplication of vectors by introducing a spectral basis of mutually annihiliating… CONTINUE READING

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## ABSTRACT Title of Document: CLIFFORD ALGEBRA: A CASE FOR GEOMETRIC AND ONTOLOGICAL UNIFICATION

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## Geometry of Moving Planes

View 1 Excerpt

#### References

##### Publications referenced by this paper.

Showing 1-10 of 15 references

## Geometric Algebra in Linear Algebra and Geometry

View 7 Excerpts

Highly Influenced

## and R

View 7 Excerpts

Highly Influenced

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

View 4 Excerpts

Highly Influenced

## Geo-Metric-Affine-Projective Computing

View 3 Excerpts

## The Missing Spectral Basis in Algebra and Number Theory

View 1 Excerpt

## Vahlen Matrices for Non-definite Metrics, in Clifford Algebras with Numeric and Symbolic Computations

View 1 Excerpt

## Clifford Algebras and the Classical Groups

View 1 Excerpt

## Geometric Algebra and Möbius Sphere Geometry as a Basis for Euclidean Invariant Theory, Editor: N.L. White, Invariant Methods in Discrete and Computational Geometry: 245–256

View 2 Excerpts

## Clifford Algebras and Spinors for Arbitrary Braids

View 2 Excerpts

## Periodicity of Clifford Algebras and Generalized Möbius Transformations

View 1 Excerpt