is it possible to calculate inverse of A-B, i have calculated inverse of A and B already.
A and B are matrices
is it possible to calculate inverse of A-B, i have calculated inverse of A and B already.
A and B are matrices
You can express $(A-B)^{-1} = -(B-A)^{-1}$ in terms of either matrix and the inverse of the other matrix as a formal power series; however, the convergence of these series are not guaranteed. $ \begin{eqnarray} (A-B)^{-1} &=& \left(A(I-A^{-1}B)\right)^{-1} \\ &=& \left(I-A^{-1}B\right)^{-1}A^{-1} \\ &=& +A^{-1} + A^{-1}BA^{-1} + A^{-1}BA^{-1}BA^{-1} + ... \\ &=& -B^{-1} - B^{-1}AB^{-1} - B^{-1}AB^{-1}AB^{-1} - ... \end{eqnarray} $