Introduction to Geometric Algebras

Abstract

Everybody knows that the real number field IR can be extended to the complex number field ℂ = IR[i] by introducing an imaginary unit i with the property that i² = −1. But few mathematicians consider the extension of the real number system by a unipotent u defined by u ≠ ±1 and u² = 1, perhaps because the resulting hyperbolic number system U is no longer a field but a commutative ring with unity.