Real functions Functions of several real variables Concept

Jacobian matrix

Builds on Partial derivative Total derivative

Summary

Let $U \subseteq \mathbb{R}^n$ be open. The Jacobian matrix of a map $f \colon U \to \mathbb{R}^m$ at a point $a$ is the $m \times n$ matrix of all first partial derivatives $\partial f_i / \partial x_j$ at $a$ . When $f$ is differentiable at $a$ , it is the matrix of the total derivative $Df(a)$ in the standard bases.

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Tag	`047NDTEPCV`
URI	`m2://047NDTEPCV`
Aliases	`jacobian`, `derivative-matrix`
Kind	concept
Writing	W1 stated
MSC	26B10
Uses	Partial derivative, Total derivative
Same as	Wikidata Q506041 Wikipedia Jacobian matrix and determinant

Jacobian matrix

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