雅可比矩阵 Jacobian matrix and determinant
在矢量分析中，雅可比矩阵是函数的一阶偏导数以一定方式排列成的矩阵，其行列式称为雅可比行列式。
在代数几何中，代数曲线的雅可比行列式表示雅可比簇：伴随该曲线的一个代数群，曲线可以嵌入其中。
它们全部都以数学家卡尔·雅可比命名；英文雅可比行列式"Jacobian"可以发音为[ja ˈko bi ən]或者[ʤə ˈko bi ən]。
Jacobian matrix
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Jacobian matrix and determinant 雅可比矩阵
（重定向自Jacobian matrix）
![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.](/Images/godic/202501/21/Jacobian_determinant_and_distortion.svg0511.png")
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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