Jordan canonical form of the Google matrix: A potential contribution to the PageRank computation

We consider the web hyperlink matrix used by Google for computing the PageRank whose form is given by A(c) = [cP + (1 - c)E]T, where P is a row stochastic matrix, E is a row stochastic rank one matrix, and c ∈ [0,1]. We determine the analytic expression of the Jordan form of A (c) and, in particular, a rational formula for the PageRank in terms of c. The use of extrapolation procedures is very promising for the efficient computation of the PageRank when c is close or equal to 1.