An Etymological Dictionary of Astronomy and Astrophysics
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→ Jacobian determinant, → Jacobian matrix.

Named after Karl Gustav Jacobi (1804-1851), a German mathematician who did important work on elliptic functions, partial differential equations, and mechanics. The "Jacobian" first appeared in an 1815 paper of the French mathematician Augustin Louis Cauchy (1789-1857), but Jacobi did write a detailed memoir about it in 1841.

The determinant of a → Jacobian matrix formed by the n² → partial derivative s of n functions of n variables.

→ Jacobian; → determinant.

In → vector calculus, the matrix of all → first-order partial derivatives of a vector-valued → function.

→ Jacobian; → matrix.