Geometric algebra: Difference between revisions

'''Geometric algebra''' is an otheranother name for [[wp:Clifford algebra|Clifford algebra]]s and it's basically an algebra containing a vector space <math>\mathcal{V}</math> and obeying the following axioms:

There are a few simple examples of geometric algebras. A trivial one for instance is simply <math>\R</math>, where <math>\mathcal{V} = \R</math>. The complex numbers also form a geometric algebra, where the vector space is the one-dimensional space of all purely imaginary numbers. An otherAnother example is the space of [[Quaternion type|quaternions]], where the vector space is the three-dimensional space of all linear combinations of <math>(i, j, k)</math>.