Meanings
plural Grassmann algebras
- algebraA 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
Synonyms & antonyms
nounA 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.
Origin
Named after Hermann Grassmann (1809–1877), a German polymath.
Full word history & related roots →Cite this entry
Grassmann algebra. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Grassmann%20algebra
“Grassmann algebra.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Grassmann%20algebra. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “Grassmann algebra,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Grassmann%20algebra.
Source: Grassmann algebra on Wiktionary, CC BY-SA 4.0.