Suppose, I have a matrix $(A-\lambda B)^{-1}$, Where $A$,$B$ are matrices and $\lambda$ is constant. It could be expanded via the following expression:
$(A(I-\lambda A^{-1}B))^{-1}$ = $(I-\lambda A^{-1}B)^{-1}$$A^{-1}$
So my question is, under what condition, $(I-\lambda A^{-1}B)^{-1}$ could be approximated as $I+\lambda A^{-1}B + ...$ ?
Thanks a lot :)