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

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

With the transformations and the Jacobian for three variables, we are ready to establish the theorem that describes change of variables for triple integrals.

From Textbooks • Mar. 30, 2016

Find the Jacobian of the transformation given in Example 5.66.

From Textbooks • Mar. 30, 2016

One of Moh’s specialties is the Jacobian conjecture, and Zhang was eager to work on it.

From The New Yorker • Jan. 26, 2015

Thus when the three minors of ∂F/∂x, ∂F/∂y, ∂F/∂z in the Jacobian determinant are all zero, there exists a functional relation connecting u and v only.

From Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 4 "Diameter" to "Dinarchus" by Various