Spectral ranking

This note tries to attempt a sketch of the history of spectral ranking—a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between entities. Albeit recently made famous by the ample press coverage of Google’s PageRank algorithm, spectral ranking was devised more than sixty years ago, almost exactly in the same terms, and has been studied in psychology, social sciences, and choice theory. I will try to describe it in precise and modern mathematical terms, highlighting along the way the contributions given by previous scholars.