106709 – Nonnegative Matrices – Theory and Applications

Lecturer: Prof. Abraham Berman

Preliminaries
· Basic Matrix Theory
· Basic Graph Theory
· Convex Cones

Theory
· The Perron-Frobenius Theorem
· Primitive Matrices
· Stochastic Matrices
· Semigroups of Nonnegative Matrices
· M-Matrices
· Completely Positive Matrices
· Inverse Eigenvalue Problems

Applications
· Iterative Methods in Numerical Analysis
· Markov Chains
· Input-Output Analysis in Economics
· The Linear Complementarity Problem
· Co-Positive Optimization
· The Mathematics behind Page Rank
· A Nonnegative Model for TCP
· A Game of Numbers

Bibliography
The course will be based on recent research papers and on the following books:
· R.B. Bapat and T.E.S. Raghavan, Nonnegative Matrices and Applications, Encyclopedia of
· Mathematics and its Applications (No. 64), Cambridge University Press, 1997.
· Abraham Berman and Robert J. Plemmons , Nonnegative Matrices in the Mathematical Sciences,
· Classics in Applied Mathematics, SIAM, 1994.
· Abraham Berman and Naomi Shaked-Monderer, Completely Positive Matrices, World Scientific, 2003.
· Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge University Press, 1990.
· Henryk Minc, Nonnegative Matrices, Wiley, 1988