Jacobian matrix and determinant

Matrix of partial derivatives of a vector-valued function

In vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals the number of components of function values, then its determinant is called the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian.

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