Jacobian matrix and determinant - Wikipedia
https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinantIn vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature.
Jacobian -- from Wolfram MathWorld
mathworld.wolfram.com/Jacobian.htmlthe Jacobian matrix, sometimes simply called "the Jacobian" (Simon and Blume 1994) is defined by. The determinant of is the Jacobian determinant (confusingly, often called "the Jacobian" as well) and is denoted. The Jacobian matrix and determinant can be computed in the Wolfram Language using. Taking the differential.