Jacobian
Also: Jacobian matrix, Jacobian determinant
For f: ℝⁿ → ℝᵐ, the m×n matrix J with Jᵢⱼ = ∂fᵢ/∂xⱼ, the best linear approximation of f near a point. For square J, |det J| is the local volume-change factor, which normalizing flows rely on.
Jᵢⱼ = ∂fᵢ / ∂xⱼ
Example
For f(x, y) = (x², xy), J = [[2x, 0], [y, x]]. At (1, 2) that is [[2, 0], [2, 1]] with determinant 2, so f doubles the area of a tiny patch there.