trace of the inverse of an Hermitian matrix

Hi all,

I need to derive a closed form for $\displaystyle Tr\{A^{-1}\}$, where A is a NxN Hermitian matrix.

A can be written as the sum of a Toeplitz matrix T and another Hermitian (non-Toeplitz) matrix C: $\displaystyle A=T+C$.

In the document: http://ee.stanford.edu/~gray/toeplitz.pdf

I've found a relation (theorem 5.2c, pag 63) which allows me to obtain an asymptotic result for $\displaystyle Tr\{T^{-1}\}$.

Do you know any result which allows me to obtain something useful about $\displaystyle Tr\{A^{-1}\}=Tr\{(T+C)^{-1}\}$ (assuming that I know $\displaystyle Tr\{T^{-1}\}$)?

Thanks a lot!

Francesco