Group Inverses of M-Matrices and Their Applications

ISBN-13: 9780367380489 / Angielski / Miękka / 2019 / 332 str.

Stephen J. Kirkland; Michael Neumann

Opis

Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Collecting diverse results into a single volume, this self-contained book highlights the importance and utility of the group inverses of M-matrices in several application areas. The authors emphasize the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. They show how group inverses offer valuable insight into each of these areas.

Spis treści

Motivation and Examples. The Group Inverse. Group Inverses and Derivatives of Matrix Functions. Perron Eigenpair in Demographic Applications. The Group Inverse in Markov Chains. Mean First Passage Times for Markov Chains. Applications of the Group Inverse to Laplacian Matrices. Computing the Group Inverse. Bibliography.

O autorze

Stephen J. Kirkland is a Stokes Professor at the National University of Ireland, Maynooth. He is editor-in-chief of Linear and Multilinear Algebra and serves on the editorial boards of several other journals. Dr. Kirkland’s research interests are primarily in matrix theory and graph theory, with an emphasis on the interconnections between these two areas.

Michael Neumann was the Stuart and Joan Sidney Professor of Mathematics and a Board of Trustees Distinguished Professor at the University of Connecticut. Dr. Neumann published more than 160 mathematical papers, mainly in matrix theory, numerical linear algebra, and numerical analysis.