Ok, so, given that, $\displaystyle C^{-1} = LD^{-1}L^{-1}$, and $\displaystyle C$ is a real valued non-singular $\displaystyle n$ x $\displaystyle n$ matrix, $\displaystyle D$ is the diagonal matrix of $\displaystyle C$'s $\displaystyle n$ distinct real non-zero eigenvalues, and $\displaystyle L$ have as columns a linearly independent set of eigenvectors in the order given by eigenvalues down D's diagonal, how do I find eigenvalues and the corresponding eigenspaces for $\displaystyle C^{-1}$ ?

Is it just the normal method $\displaystyle [A - \lambda I_n]$? (I can't see a result out of this method...)

Your help is much appreciated