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

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

Now we can calculate the Jacobian for the transformation:

From Textbooks ● Mar. 30, 2016

The Jacobian conjecture, a problem in algebraic geometry that was introduced in 1939 and is still unsolved, stipulates certain simple conditions that, if satisfied, enable someone to solve a series of complicated equations.

From The New Yorker ● Jan. 26, 2015

But among the remaining parts of Pure Mathematics we have the theory of Elliptic Functions and of the Jacobian and Abelian Functions, and the theory of Differential Equations, including of course Partial Differential Equations.

From Autobiography of Sir George Biddell Airy by Airy, George Biddell