Jacobian matrix and determinant

A nonlinear map f : R2 → R2 sends a small square to a distorted parallelepiped close to the image of the square under the best linear approximation of f near the point.

In vector calculus, the Jacobian matrix (/dʒᵻˈkoʊbiən/, /jᵻˈkoʊbiən/) is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square matrix, both the matrix and its determinant are referred to as the Jacobian in literature.

单词	Jacobian determinant
释义	Jacobian determinant 英语百科 Jacobian matrix and determinant In vector calculus, the Jacobian matrix (/dʒᵻˈkoʊbiən/, /jᵻˈkoʊbiən/) is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square matrix, both the matrix and its determinant are referred to as the Jacobian in literature.
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Jacobian determinant

Jacobian matrix and determinant