By David Hestenes
Matrix algebra has been known as "the mathematics of upper arithmetic" [Be]. we predict the root for a greater mathematics has lengthy been to be had, yet its versatility has rarely been favored, and it has now not but been built-in into the mainstream of arithmetic. We confer with the process ordinarily known as 'Clifford Algebra', even though we desire the identify 'Geometric Algebm' advised by way of Clifford himself. Many designated algebraic structures were tailored or built to specific geometric relatives and describe geometric buildings. specifically outstanding are these algebras which were used for this function in physics, specifically, the process of advanced numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential kinds. each one of those geometric algebras has a few major virtue over the others in sure functions, so not anyone of them presents an sufficient algebraic constitution for all reasons of geometry and physics. while, the algebras overlap significantly, so that they offer a number of diverse mathematical representations for person geometrical or actual ideas.