Grassmann algebra

Etymology
Named after (1809–1877), a German polymath.

Noun

 * 1)  A direct sum with an exterior product of multivector spaces which are all based on a same underlying finite-dimensional vector space. The associative algebra of sums and exterior products of scalars, vectors, blades, multivectors, and hybrid (i.e., non-homogeneous) sums of multivectors of different grades.
 * If a Grassmann algebra&rsquo;s first grade consists of vectors of dimension n, then the algebra has n grades and $$2^n$$ dimensions.