Inverse M-Matrices and Ultrametric Matrices
Author:   Claude Dellacherie ,  Servet Martinez ,  Jaime San Martin
Publisher:   Springer International Publishing AG
Edition:   2014 ed.
Volume:   2118
ISBN:  

9783319102979


Pages:   236
Publication Date:   04 December 2014
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Inverse M-Matrices and Ultrametric Matrices


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Overview

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.

Full Product Details

Author:   Claude Dellacherie ,  Servet Martinez ,  Jaime San Martin
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   2014 ed.
Volume:   2118
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783319102979


ISBN 10:   3319102974
Pages:   236
Publication Date:   04 December 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

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.

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