The matrix that arranges the first-order partial derivatives of a function of a vector.
vector y is a function f of vector x:
vector y = f(vector x)
vector x = [x1, x2, ..., xn]
vector y = [y1, y2, ..., ym]
Jacobian matrix:
J = [∂f/x1, ∂f/x2, ..., ∂f/xn]
= [∂y1/x1, ∂y1/x2, ..., ∂y1/xn
∂y2/x1, ∂y2/x2, ..., ∂y2/xn
.....
∂ym/x1, ∂ym/x2, ..., ∂ym/xn]
(The above figure of formula is from Wikipedia: Jacobian matrix and determinant)
References:
Jacobian Matrix (Wikipedia) 雅可比矩陣 (維基百科)
Autograd: Automatic Differentiation (PyTorch Official Tutorial)
