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Jacobian matrix includes all first-order partial derivatives of the given function. The determinant of this matrix is called Jacobian, which reveals how much the transformed area is changed in size. Moreover, Jacobian matrix is used for linearization of nonlinear functions. The formulas and examples are included here. Some codes of Python are given too.
using Jacobian matrix for root finding of vector functions are reviewed here, which is called the Newton-Raphson method. Examples are also included with some Python codes.
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