S. Friedland et al., ROW SUMS AND INVERSE ROW SUMS FOR NONNEGATIVE MATRICES, SIAM journal on matrix analysis and applications, 15(4), 1994, pp. 1157-1166
For a nonnegative, irreducible matrix A, the grading of the row sums v
ector and the grading of the Perron vector are used to predict the gra
ding of the row sums vector of (I - A)-1. This has applications to Mar
kov chains.