Suppose A_{N \times N} and B_{N+1 \times N+1} are two symetric positive definte matrix such that:  B=<br />
 \begin{bmatrix}<br />
        &   & &  & b \\<br />
        & A & &  & b \\<br />
        &   & &  &b  \\<br />
       b&  b& ...&b& b^{'}<br />
 \end{bmatrix}
Let use define operator SUM for a matrix G_{k \times k}such that:
SUM(G)=\Sigma_{i=1}^{k}\Sigma_{j=1}^{k}G_{ij} then:
SUM(B^{-1})=\frac{SUM(A^{-1})+b^{'}-2bb^{'}SUM(A^{-1})}{1-b^{2}b^{'}SUM(A^{-1})}
wher G^{-1} means inverse of the matrix G