Google pageranking problem: The model and the analysis (Q989122)

For a given square complex matrix \(A\) and nonzero complex vectors \(x\) and \(v\) such that \(Ax=\lambda x\) and \(v^* x = 1\) the authors determine the eigenvalues, the Jordan blocks, and a distinguished left \(\lambda\)-vector of \(A(c)=c A + (1-c) \lambda x v^*\) as a function of the complex variable \(c\). As a special case of this result they obtain a complex analog of the Page-Rank for the web hyperlink matrix \(G(c)\) with a complex parameter \(c\).