Grassmann algebra

== English == === Etymology === Named after Hermann Grassmann (1809–1877), a German polymath. === 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. ==== Synonyms ==== exterior algebra ==== Hypernyms ==== associative algebra graded algebra ==== Further reading ==== exterior algebra