Phrase guide

Clifford 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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Pronunciation

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1

noun

Meaning 1

A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of γi (with i ranging from, say, 1 to n) such that the square of each γi is fixed to be either +1 or −1, depending on each i, and such that any product γiγj anticommutes when its factors are distinct (i.e., when i ne j).

Definition source: English Wiktionary via Wiktextract

Qualifier: mathematical physics

Topics: algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after William Kingdon Clifford (1845–1879), an English mathematician and philosopher.

Across languages

Translations

9 source translations are retained for this English entry.

  • Chinese Mandarin: 克利福德代数 (Kèlìfúdé dàishù) — unital associative algebra which generalizes the algebra of quaternions
  • French: algèbre de Clifford — unital associative algebra which generalizes the algebra of quaternions
  • German: Clifford-Algebra — unital associative algebra which generalizes the algebra of quaternions
  • Italian: algebra di Clifford — unital associative algebra which generalizes the algebra of quaternions
  • Japanese: クリフォード代数 (Kurifōdo-daisū) — unital associative algebra which generalizes the algebra of quaternions
  • Korean: 클리퍼드 대수 (Keullipeodeu daesu) — unital associative algebra which generalizes the algebra of quaternions
  • Portuguese: álgebra de Clifford — unital associative algebra which generalizes the algebra of quaternions
  • Russian: алгебра Клиффорда — unital associative algebra which generalizes the algebra of quaternions
  • Spanish: álgebra de Clifford — unital associative algebra which generalizes the algebra of quaternions