Geometric matrix algebra

Extensors in Geometric Algebra

This paper, the third in a series of three introduces the basics of the theory of extensors that are need for the a theory of multvector and extensor fields in arbitrary manifolds, developed in a following series of five papers. Key notions such as the extension and generalization operators of a given linear operator (a (1, 1)-extensor) acting on a real vector space V are introduced and studied...

Projective Geometric Algebra

Oriented Conformal Geometric Algebra

In [12] Stolfi developed a complete theory of Oriented Projective Geometry. He showed that assigning meaning to the sign of an otherwise homogenous representation of geometry could provide a multitude of benefits. This paper extends his work by applying the same approach to Conformal Geometric Algebra. Oriented Conformal Geometric Algebra allows intuitive manipulation of such concepts as half-s...

Universal Geometric Algebra

Alfred North Whitehead promoted the idea of UNIVERSAL ALGEBRA in his monumental treatise of 1897 [1]. He proposed two candidates for this lofty title, the algebra of Boole and Grassmann’s Algebra of Extension. Boolean algebra has since secured universality status in Set Theory and Symbolic Logic, although only the former is universally known and used by mathematicians. However, Whitehead’s work...

Geometric Algebra – Leibnitz’ Dream

1. Historical Developments About 150 years ago, in 1844, the German high school teacher Hermann Grassmann published an ambitious work entitled The Linear Extension Theory, A New Branch of Mathematics. For Grassmann this was indeed The Branch of mathematics, which in his own words “far surpasses” all others. His subsequent work Geometric Algebra won the prize of 45 gold ducats set out by the Pri...