Phrase guide

Grassmann algebra

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 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.

Definition source: English Wiktionary via Wiktextract

Topics: algebra, mathematics, sciences

Examples

  • If a Grassmann algebra’s first grade consists of vectors of dimension n, then the algebra has n grades and 2n dimensions.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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