Grassmann algebra

English

Etymology

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

Noun

Grassmann algebra (plural Grassmann algebras)

1. (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 $2^{n}$ dimensions.

Synonyms

• exterior algebra

Hypernyms

• associative algebra
• graded algebra

Further reading

• exterior algebra