Is that a catchy title or what? No, and the story doesn’t involve Philip Marlowe or Sam Spade. See The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google by Kurt Bryan and Tanya Leise. Here’s the abstract.

“Googleâ€™s success derives in large part from its PageRank algorithm, which ranks the importance of webpages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course. Instructors may assign this article as a project to more advanced students, or spend one or two lectures presenting the material with assigned homework from the exercises. This material also complements the discussion of Markov chains in matrix algebra. Maple and Mathematica ï¬les supporting this material can be found at http://www.rose-hulman.edu/~bryan/google.html

“.

These techniques, and the mathematics behind them, are important in modeling many kinds of social phenomena.