Jacobian

American  

[juh-kohb-ee-uhn] / dʒəˈkoʊb i ən /

noun

• Jacobians
  plural

1. Mathematics. a matrix whose entries are all the first-order partial derivatives of a vector-valued function, or the determinant of that matrix.

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adjective

1. Mathematics. relating to any of the mathematical concepts developed by Karl Gustav Jakob Jacobi.

Jacobian British  

/ dʒəˈkəʊbɪən /

noun

1. maths a function from n equations in n variables whose value at any point is the n x n determinant of the partial derivatives of those equations evaluated at that point

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Other Word Forms

Noun Inflected Forms

• Jacobians
  plural

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Etymology

Origin of Jacobian

named after Karl Gustav Jacob Jacobi (1804–51), German mathematician.

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Example Sentences

See Examples For:

Jacobian

For those of us who haven’t thought about math since high school, the recent events have taught us about Erdős problems, the Jacobian conjecture and a phenomenon known as “finite-time blowup.”

From The Wall Street Journal ● Sep. 12, 2026

If the Jacobian determinant is always a constant number that is not zero, then the function never folds or crushes space around a particular point.

From Science Daily ● Aug. 6, 2026

The next head-spinning result arrived when Anthropic’s Fable model found a counterexample to the Jacobian conjecture, a famously treacherous problem that had defied mathematicians for 87 years.

From The Wall Street Journal ● Aug. 1, 2026

LSU’s rotation on the interior defensive line this season also includes junior Mekhi Wingo, redshirt junior Jacobian Guillory and senior West Virginia transfer Jordan Jefferson.

From Seattle Times ● Aug. 24, 2023

Biblical critics are inclined, however, to accept in its strict sense the translation of the Jacobian divines.

From The Superstitions of Witchcraft by Howard Williams

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