Group Inverses of M-Matrices and Their Applications

This book presents a comprehensive treatment of nonnegative and M-matrices and their application in matrix analysis, stochastic processes, graph theory, electrical networks, and demographic models. It summarizes the past 30 years of results and highlights connections between the use of group inverse theory and problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. The authors examine a variety of techniques and demonstrate how the group inverse can be computed using the shuffle and Hartwig algorithm and the divide and conquer method.