Word Pronunciation & Dictionary

jacobi identity

Word Rarity Rare

Frequency: Zipf frequency 2.73 in modern English

Syllables: ja-co-bi i-den-ti-ty
IPA

29

Scrabble Score

14

Letters

6

Syllables

11

Unique Chars

Meaning

noun

Given a binary operation × defined on a set S which also has additive operation + and additive identity 0, the property that a × (b×c) + b × (c×a) + c × (a×b) = 0 for all a, b, c in S.

Countable; Uncountable

Example Sentences

"We give here two proofs of the Jacobi identity for the generalized Poisson bracket defined in Eq. (13.69a)."
"2004, James Lepowsky, Haisheng Li, Introduction to Vertex Operator Algebras and Their Representations, Springer (Birkhäuser), page 12, As we have already mentioned, the Jacobi identity is actually the generating function of an infinite list of generally highly nontrivial identities, and one needs many of these individual componenent identities in working with the theory."
"It is sufficient to test the Jacobi identity against three linear functions [354] (this reference also provides a code for evaluating Jacobi identities)."

Etymology

After German mathematician Carl Gustav Jakob Jacobi (1804-1851).

Usage

Inflected Forms

Jacobi identities (plural)

Phrases

super Jacobi identity

Questions

What does jacobi identity mean?: Given a binary operation × defined on a set S which also has additive operation + and additive identity 0, the property that a × (b×c) + b × (c×a) + c × (a×b) = 0 for all a, b, c in S.
Where does jacobi identity come from?: After German mathematician Carl Gustav Jakob Jacobi (1804-1851).

How to pronounce jacobi identity

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