Inverse M-Matrices and Ultrametric Matrices / by Claude Dellacherie, Servet Martinez, Jaime San Martin.

Format:

Book

Author/Creator:

Dellacherie, Claude, author.

Martínez, Servet, author.

San Martín, Jaime, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2118.

Lecture Notes in Mathematics, 0075-8434 ; 2118

Language:

English

Subjects (All):

Potential theory (Mathematics).

Distribution (Probability theory).

Mathematics.

Potential Theory.

Probability Theory and Stochastic Processes.

Game Theory, Economics, Social and Behav. Sciences.

Local Subjects:

Potential Theory.

Probability Theory and Stochastic Processes.

Game Theory, Economics, Social and Behav. Sciences.

Physical Description:

1 online resource (X, 236 pages 14 illustrations).

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2014.

System Details:

text file PDF

Summary:

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.

Contents:

Inverse M - matrices and potentials

Ultrametric Matrices

Graph of Ultrametric Type Matrices

Filtered Matrices

Hadamard Functions of Inverse M - matrices

Notes and Comments Beyond Matrices

Basic Matrix Block Formulae

Symbolic Inversion of a Diagonally Dominant M - matrices

Bibliography

Index of Notations

Index.

Other Format:

Printed edition:

ISBN:

9783319102986

Access Restriction:

Restricted for use by site license.