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

He found an example of a function in three dimensions which has a constant Jacobian determinant of -2, and which moves multiple input points to the same output point, so it is not reversible.

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 5.66.

From Textbooks ● Mar. 30, 2016

As this goes on the equator of these Jacobian figures becomes more and more elliptic, so that the shape is considerably elongated in a direction at right angles to the axis of rotation.

From Darwin and Modern Science by A. C. (Albert Charles) Seward