Proof of Affine Invariance for Newton's Method

Students often struggle to see how the matrix

A

cancels, forgetting that for the inverse of a product,

(AB)^{-1} = B^{-1}A^{-1}

. They mistakenly try to invert

A

and

Df

individually without considering the order of operations in the matrix product.

Institutional Reference: Fundamentals of Optimization