Grassmann algebra
nounEtymology Named after Hermann Grassmann (1809–1877), a German polymath.
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Algebra, Mathematics, Sciences 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 2ⁿ dimensions.
- Synonyms
- exterior algebra
- Hypernyms
- associative algebra, graded algebra