trace of the inverse of an Hermitian matrix

Hi all,

I need to derive a closed form for , 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: .

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 .

Do you know any result which allows me to obtain something useful about (assuming that I know )?

Thanks a lot!

Francesco