Standard Lemma guide

Jacobian

adj · noun · 6 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.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

  • yä-kō'-bi-un
  • /jɑːˈkəʊ.bi.ən/
  • /d͡ʒəˈkoʊ.bi.ən/
  • US: Recorded audio is listed in the source snapshot.

1

adj

Meaning 1

Used to specify certain mathematical objects named in honour of C. G. J. Jacobi.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Examples

  • The Jacobian matrix has partial derivatives as its entries.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

adj

Meaning 2

Of or relating to the biblical Jacob.

Definition source: English Wiktionary via Wiktextract

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: Jacobic

Antonyms: none provided

3

adj

Meaning 3

Alternative letter-case form of Jacobian.

Definition source: English Wiktionary via Wiktextract

Usage: alt-of, not-comparable

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

4

noun

Meaning 4

A Jacobian matrix or its associated operator.

Definition source: English Wiktionary via Wiktextract

Topics: calculus, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

5

noun

Meaning 5

The determinant of such a matrix.

Definition source: English Wiktionary via Wiktextract

Topics: calculus, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

6

noun

Meaning 6

Alternative letter-case form of Jacobian.

Definition source: English Wiktionary via Wiktextract

Usage: alt-of

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

From Jacobi + -an, after Carl Gustav Jacob Jacobi, a German mathematician of the 19th century.

Etymology tree English Jacob Proto-Indo-European *-nós Proto-Italic *-nos Latin -nus Latin -ānus Latin -iānusbor. English -ian English Jacobian From Jacob + -ian.

Across languages

Translations

21 source translations are retained for this English entry.

  • Bulgarian: на Якоби (na Jakobi) — in honor of Jacobi
  • German: Jacobi- — in honor of Jacobi
  • Spanish: jacobiano — in honor of Jacobi
  • Bulgarian: матица на Якоби (matica na Jakobi) — Jacobian matrix
  • Bulgarian: Якобиан (Jakobian) — Jacobian matrix
  • German: Jacobi-Matrix — Jacobian matrix
  • German: Funktionalmatrix — Jacobian matrix
  • German: Ableitungsmatrix — Jacobian matrix
  • Hebrew: מטריצת יעקובי (matrítzat ya'akóbi) — Jacobian matrix
  • Polish: macierz Jacobiego — Jacobian matrix
  • Russian: матрица Якоби (matrica Jakobi) — Jacobian matrix
  • Spanish: matriz jacobiana — Jacobian matrix
  • Bulgarian: Якобиан (Jakobian) — the determinant of the Jacobian matrix
  • Bulgarian: детерминанта на Якоби (determinanta na Jakobi) — the determinant of the Jacobian matrix
  • German: Jacobi-Determinante — the determinant of the Jacobian matrix
  • German: Funktionaldeterminante — the determinant of the Jacobian matrix
  • Hebrew: יעקוביאן (ya'akobián) — the determinant of the Jacobian matrix
  • Polish: jakobian — the determinant of the Jacobian matrix
  • Russian: якобиан (jakobian) — the determinant of the Jacobian matrix
  • Spanish: determinante jacobiano — the determinant of the Jacobian matrix
  • Spanish: jacobiano — the determinant of the Jacobian matrix
Real reading context

Jacobian in complete knowledge articles