Overview
- Provides a unified algebraic and probabilistic approach
- Describes graphs and algorithms for inverse M-matrices
- Gives examples and fields of applications of M-matrices
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2118)
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Table of contents (6 chapters)
Keywords
About this book
The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.
Authors and Affiliations
Bibliographic Information
Book Title: Inverse M-Matrices and Ultrametric Matrices
Authors: Claude Dellacherie, Servet Martinez, Jaime San Martin
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-10298-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Softcover ISBN: 978-3-319-10297-9Published: 04 December 2014
eBook ISBN: 978-3-319-10298-6Published: 14 November 2014
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 236
Number of Illustrations: 14 b/w illustrations
Topics: Potential Theory, Probability Theory and Stochastic Processes, Game Theory, Economics, Social and Behav. Sciences