Can Newton's method be used to find the root of a function f : $\mathbb{R}^n\to\mathbb{R}^m$. Can anyone provide a proof for this?
(I have checked the method of solving system of equations with newton's method, but in all the cases that I could find, the number of equations were equal to the number of variables. In this case however, this is not true and thus the Jacobian would not be invertible.)
Edit: This paper does what I am looking for, but I can't seem to understand the assumptions made in the proof. Whether they are trivial and always valid, or whether they are valid only in some special cases.