Inverse m-matrices and ultrametric matrices /

Inverse m-matrices and ultrametric matrices /

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Bibliographic Details
Author / Creator:	Dellacherie, Claude, author.
Imprint:	Cham [Switzerland] : Springer, [2014]
Description:	1 online resource (x, 236 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 1617-9692 ; 2118 Lecture notes in mathematics (Springer-Verlag) ; 2118.
Subject:	Matrices. Inverse problems (Differential equations) Inverse problems (Differential equations) Matrices.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11089764

Hidden Bibliographic Details
Other authors / contributors:	Martínez, Servet, author. San Martín, Jaime, author. SpringerLink (Online service)
ISBN:	9783319102979 3319102974 9783319102986 3319102982
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed November 19, 2014).
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.
Other form:	Printed edition: 9783319102979
Standard no.:	10.1007/978-3-319-10298-6

Table of 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.