Web information retrieval (IR) is more challenging than the traditional IR because of the huge number of web pages (in the order of 10 billions). In the IR method research, each webpage is represented as a node of in a directed graph. The directed edges connecting these nodes represent the hyperlinks between the pages. In 1998 Google co-founders Sergey Brin and Larry Page introduced the Google matrix for the computation of the PageRank which is the heart of Google's software. The idea of PageRank, which is a ranking of web pages, is that links from important pages should carry more weight than less important ones, and the significance of a link from any source page should be scaled by the number of pages the source is linking to. To carry out this basic idea, they defined a "raw" Google matrix P.

In this talk we introduce the Google matrix G, which is a perturbation of the raw Google matrix P for the computation of the PageRank, and we also present a recent result on the spectrum of the Google matrix. We give an elementary proof of the spectrum result, based on a well known determinant identity in linear algebra.

Dr. Ding received the Ph.D. degree in applied mathematics from Michigan State University, USA in 1990 after receiving his B.S. and M.S. degrees in computational mathematics from Nanjing University, China in 1982 and 1984, respectively. Upon graduation, he joined the Department of Mathematics at the University of Southern Mississippi, and was promoted to the rank of Full Professor in 1999. He has published about 70 research papers on more than 25 international refereed journals in the areas of ergodic theory of chaos, mathematical programming, linear algebra, operator theory, and mathematical education. His current research interests include applications of chaos theory to wireless communications and mesh-less methods in scientific computing.

He is a co-author of a recent text titled Statistical Properties of Deterministic Systems, Tsinghua University Press, 2006. He received a University Research Award, a University Teaching Award, and a University Grand Marshal Award, all from the University of Southern Mississippi, and a Second Prize from the Chinese Composition Competition at the First Reading Festival of Jiangsu Province, China. He is a member of the editorial committee for an international journal, Numerical Mathematics.