Sei ${\displaystyle {}G\subseteq {\mathbb {K} }^{n}}$ offen und sei eine Abbildung

${\displaystyle f\colon G\longrightarrow {\mathbb {K} }^{m},\,(x_{1},\ldots ,x_{n})\longmapsto f(x_{1},\ldots ,x_{n})=(f_{1}(x_{1},\ldots ,x_{n}),\ldots ,f_{m}(x_{1},\ldots ,x_{n})),}$

gegeben, die in ${\displaystyle {}P\in G}$ partiell differenzierbar sei. Dann heißt die Matrix

${\displaystyle {}\operatorname {Jak} (f)_{P}:={\begin{pmatrix}{\frac {\partial f_{1}}{\partial x_{1}}}(P)&\ldots &{\frac {\partial f_{1}}{\partial x_{n}}}(P)\\\vdots &\ddots &\vdots \\{\frac {\partial f_{m}}{\partial x_{1}}}(P)&\ldots &{\frac {\partial f_{m}}{\partial x_{n}}}(P)\end{pmatrix}}\,}$

die Jacobi-Matrix zu ${\displaystyle {}f}$ im Punkt ${\displaystyle {}P}$.