Inverse M-matrices and ultrametric matrices /

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...

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Bibliographic Details
Main Author: Dellacherie, Claude (Author)
Corporate Author: SpringerLink (Online service)
Other Authors: Martinez, Servet, San Martin, Jaime
Format: eBook
Language:English
Published: Cham Springer International Publishing 2014.
Series:Lecture Notes in Mathematics 2118
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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.
Physical Description:1 online resource (X, 236 pages) 14 illustration.
ISBN:9783319102986
ISSN:0075-8434