Geometric Algebra with Applications in Science and Engineering

  title={Geometric Algebra with Applications in Science and Engineering},
  author={Eduardo Bayro Corrochano and Garret 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.

Some Applications of Gröbner Bases in Robotics and Engineering

  • R. Abłamowicz
  • 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.

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 classical

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.

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 mathematical

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 in

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 reciprocal

Complex and Hyperbolic Numbers

The complex numbers were grudgingly accepted by Renaissance mathematicians because of their utility in solving the cubic equation.1 Whereas the complex numbers were discovered primarily for algebraic

Geometric algebra generation of molecular surfaces

A geometric algebra method for the molecular surface generation that utilizes the Clifford-Fourier transform which is a generalization of the classical Fourier transform and is used to solve the mode decomposition process in PDE transform.

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 geometric