Matrix algebra has been referred to as "the mathematics of upper arithmetic" [Be]. we expect the foundation for a greater mathematics has lengthy been to be had, yet its versatility has rarely been liked, and it has now not but been built-in into the mainstream of arithmetic. We consult with the approach usually known as 'Clifford Algebra', although we want the identify 'Geometric Algebm' advised through Clifford himself. Many distinctive algebraic structures were tailored or built to specific geometric kinfolk and describe geometric buildings. in particular amazing are these algebras which were used for this function in physics, specifically, the procedure of advanced numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential varieties. each one of those geometric algebras has a few major virtue over the others in sure functions, so nobody of them presents an enough algebraic constitution for all reasons of geometry and physics. whilst, the algebras overlap significantly, so that they supply numerous diverse mathematical representations for person geometrical or actual rules.

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