Assume NxN matrix A of complex values. I want to calculated the sum of all elements of its inverse. Does anybody have any good idea how to do this? The problem is that calculating the inverse is computationally expensive and since I am looking only for the sum of its elements, I thought there might be something smarter to do.
Note: the real part of A is diagonal while the imaginary is a 2x2 block matrix of symmetric submatrices.