Noun
Grassmann algebra (plural Grassmann algebras)
(algebra) 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’s first grade consists of vectors of dimension n, then the algebra has n grades and
2
n
{\displaystyle 2^{n}}
dimensions.