Geometric Algebra with Applications in Science and Engineering

  title={Geometric Algebra with Applications in Science and Engineering},
  author={Eduardo Bayro Corrochano and G. Sobczyk},
Advances in Geometric Algebra Computing Lie Algebras and Geometric Algebra, Geometric Filtering, Interpolation, Optimization Geometric Algebra of Computer Vision Neural and Quatum Computing Geometric Computing in Robotics Geometric Physics 
Engineering Graphics in Geometric Algebra
The suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications, is illustrated and the potential of geometricgebra for optimizations and highly efficient implementations is included. Expand
Some Applications of Gröbner Bases in Robotics and Engineering
  • R. Ablamowicz
  • Mathematics, Computer Science
  • Geometric Algebra Computing
  • 2010
This work shows a few applications of Grobner bases in robotics, formulated in the language of Clifford algebras, and in engineering to the theory of curves, including Fermat and Bezier cubics, and interpolation functions used in finite element theory. Expand
Calculus on m -Surfaces
We apply all of the machinery of linear algebra developed in the preceding chapters to the study of calculus on an m-surface. The concept of the boundary of a surface is defined, and the classicalExpand
Applications of Clifford’s Geometric Algebra
The benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope is demonstrated from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond. Expand
From Grassmann’s vision to geometric algebra computing
What mathematicians often call Clifford algebra is calledgeometric algebra if the focus is on the geometric meaning of the algebraic expressions and operators. Geometric algebra is a mathematicalExpand
Non-euclidean and Projective Geometries
We investigate the relationship between conformal transformations in \({\mathbb{R}}^{p,q}\), studied in the previous chapter, and orthogonal transformations acting on the horosphere inExpand
Linear and Bilinear Forms
Geometric algebra is not used in this chapter. The material presented is closely related to the material in Sect. 7.1 but represents a change of viewpoint. Instead of talking about the reciprocalExpand
Linear Transformations on {\mathbb{R}}^{n}
The definition of a linear transformation on \({\mathbb{R}}^{n}\), and its natural extension to an outermorphism on all of the geometric algebra \({\mathbb{G}}_{n}\), is given. The tools of geometricExpand
Clifford algebra with mathematica
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work,Expand
Modular Number Systems
We begin by exploring the algebraic properties of the modular numbers, sometimes known as clock arithmetic, and the modular polynomials. The modular numbers and modular polynomials are based upon theExpand