# trace of the inverse of an Hermitian matrix

• Sep 7th 2010, 02:20 AM
frm
trace of the inverse of an Hermitian matrix
Hi all,
I need to derive a closed form for $Tr\{A^{-1}\}$, 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: $A=T+C$.
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 $Tr\{T^{-1}\}$.
Do you know any result which allows me to obtain something useful about $Tr\{A^{-1}\}=Tr\{(T+C)^{-1}\}$ (assuming that I know $Tr\{T^{-1}\}$)?

Thanks a lot!
Francesco