Geometric Algebra with Applications in Science and EngineeringEduardo Bayro Corrochano, Garret Sobczyk The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers. |
Contents
8 | |
Geometric Feedforward Neural Networks and Support Mul | 15 |
Boundary Collisions as Geometric Wave | 17 |
Universal Geometric Algebra | 19 |
Hyperbolic Geometry | 62 |
doublehyperbolic space | 69 |
Projective Reconstruction of Shape and Motion Using | 191 |
geometric invariants | 206 |
Quantum and Neural Computing | 278 |
Modern Geometric Calculations in Crystallography | 372 |
Applications of Geometric Algebra in Physics and Links | 433 |
22 | 462 |
535 | |
583 | |
Other editions - View all
Geometric Algebra with Applications in Science and Engineering Eduardo Bayro Corrochano No preview available - 2001 |
Geometric Algebra with Applications in Science and Engineering Eduardo Bayro Corrochano,Garret Sobczyk No preview available - 2012 |
Common terms and phrases
affine plane algorithm angles arbitrary axis Birkhäuser Boston 2001 bivector bracket calibration camera Clifford algebra coefficients complex components conformal geometry conformal representant conformal transformation coordinates corresponding defined definition denote derivative differential dimension double quaternions dual E. B. Corrochano elements equation Euclidean space example expression FIGURE follows function geometric algebra geometric product given gives Hestenes homogeneous model horosphere hyperbolic hyperplane identity image plane inner product intersection invariant inverse joint key frames Lie algebra linear operator mapping matrix Minkowski motion multiplication multivector null cone null vectors obtain oriented orthogonal outer product parameters paravector perpendicular point at infinity position problem projective geometry projective split proof prove pseudoscalar quantum reciprocal reconstruction relation represented result robot rotation rotors scalar sequence simplify solve spacetime sphere spin spinor subspace tangent space task trajectory theorem translation triangle trivectors versor world points