Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
This chapter intends to be a survey on Exterior Algebra. This algebra is attributed to Hermann Grassmann [Die lineare Ausdehnungslehre, ein neuer Zweig der Mathematik, 1842], and it is formed by two operators: the exterior product and inner product. William K. Clifford unified both products under the geometric product operator and David Hestenes improved the geometric and computer aspects of Geometric algebra. Here, we review the main operators and their properties, as well as their application in the representation of lines and planes.
Keywords:
Bivector, Differential forms, Differentiation, Dot product, Dual space, Exterior product, Geometric algebra, Geometric product, Grassmann algebra, Inner product, Norm, Oriented plane, Orthogonal basis, Reflections, Rigid body motions, Rotations.
Recommended Chapters
We recommend
Authors:Bentham Science Books