I am looking for different representations of the inverse of a matrix as a power series. One obvious candidate is the Von Neumann series which is given
$$A^{-1} = \sum_{k=0}^{\infty} (I-A)^k$$
However the series above converges only of A is Positive Definite and $\|A\| \leq 1$. Are there other series that do not explicitly require the matrix to be Positive Definite ? I am okay with the spectral norm bound as that requires only multiplication by a scalar.