Word.ws English Dictionary

Grassmann algebra

Grassmann algebra noun: 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.

Noun

Grassmann algebra (plural Grassmann algebras)

  1. 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

Synonyms of Grassmann algebra

  • exterior algebra

Forms of Grassmann algebra

pluralGrassmann algebras

Origin of Grassmann algebra

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

Questions about Grassmann algebra

What does Grassmann algebra mean?
Grassmann algebra means 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.
What part of speech is Grassmann algebra?
Grassmann algebra is a noun.
What is the plural of Grassmann algebra?
The plural of Grassmann algebra is Grassmann algebras.

Words near Grassmann algebra in the dictionary

  1. grasslike
  2. grassling
  3. grasslings
  4. Grassman
  5. Grassmann
  6. Grassmann algebra
  7. Grassmann algebras
  8. Grassmann's law
  9. Grassmannian
  10. Grassmannians
  11. Grassmans

Source and license

Adapted from Wiktionary: Grassmann algebra (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “Grassmann algebra.” Word.ws, https://word.ws/grassmann_algebra. Based on Wiktionary, CC BY-SA 4.0.