Inverse M-Matrices and Ultrametric Matrices (Paperback, 2014 ed.)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2118
Release date:	November 2014
First published:	2014
Authors:	Claude Dellacherie • Servet Martinez • Jaime San Martin
Dimensions:	235 x 155 x 13mm (L x W x T)
Format:	Paperback
Pages:	236
Edition:	2014 ed.
ISBN-13:	978-3-319-10297-9
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Optimization > Game theory Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics Promotions
LSN:	3-319-10297-4
Barcode:	9783319102979

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