Es sei ${\displaystyle {}K}$ ein Körper und es seien ${\displaystyle {}f_{1},\ldots ,f_{m}\in K[X_{1},\ldots ,X_{n}]}$ Polynome. Es sei ${\displaystyle {}P\in K^{n}}$ ein Punkt. Dann heißt die Matrix

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

die Jacobi-Matrix zu ${\displaystyle {}f_{1},\ldots ,f_{m}}$ im Punkt ${\displaystyle {}P}$.