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

Etymology

Origin of Jacobian

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

Example Sentences

See Examples For:

Jacobian

You can test how “nicely” a function moves everything around in space by calculating something called the Jacobian determinant.

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

Find the Jacobian of the transformation given in Example 5.65.

From Textbooks ● Mar. 30, 2016

The mixture of this late Jacobian work with the old work of the chantry is very curious, and can be traced all over what remains of it.

From Notes and Queries, Number 180, April 9, 1853 A Medium of Inter-communication for Literary Men, Artists, Antiquaries, Genealogists, etc by George Bell