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portada Inverse M-Matrices and Ultrametric Matrices (Lecture Notes in Mathematics)
Type
Physical Book
Publisher
Author
Year
2014
Language
English
Pages
236
Format
Paperback
ISBN13
9783319102979
Edition No.
2014
Categories

Inverse M-Matrices and Ultrametric Matrices (Lecture Notes in Mathematics)

Claude Dellacherie; Servet Martinez; Jaime San Martin (Author) · Springer · Paperback

Inverse M-Matrices and Ultrametric Matrices (Lecture Notes in Mathematics) - Claude Dellacherie; Servet Martinez; Jaime San Martin

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Synopsis "Inverse M-Matrices and Ultrametric Matrices (Lecture Notes in Mathematics) "

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.

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