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Inverse M-Matrices and Ultrametric Matrices

E-BookPDF1 - PDF WatermarkE-Book
236 Seiten
Englisch
Springer International Publishingerschienen am14.11.20142014
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.mehr
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BuchKartoniert, Paperback
EUR40,65
E-BookPDF1 - PDF WatermarkE-Book
EUR39,58

Produkt

KlappentextThe 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.
Details
Weitere ISBN/GTIN9783319102986
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2014
Erscheinungsdatum14.11.2014
Auflage2014
ReiheLecture Notes in Mathematics
Reihen-Nr.2118
Seiten236 Seiten
SpracheEnglisch
IllustrationenX, 236 p. 14 illus.
Artikel-Nr.5846328
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

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