I have a square matrix $A$.
Is it possible to determine if its largest eigenvalue is smaller (by magnitude) than 1 by inspecting the matrix $(I-A)^{-1}$?
(we can assume that $I-A$ is invertible.)
EDIT: My question is quite simple, if not more specific. Obviously you could recover $A$ and compute its spectrum. But I am looking for something which is algorithmically simple...