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Inverse M-Matrices and Ultrametric Matrices / / by Claude Dellacherie, Servet Martinez, Jaime San Martin



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Autore: Dellacherie Claude Visualizza persona
Titolo: Inverse M-Matrices and Ultrametric Matrices / / by Claude Dellacherie, Servet Martinez, Jaime San Martin Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014
Edizione: 1st ed. 2014.
Descrizione fisica: 1 online resource (X, 236 p. 14 illus.)
Disciplina: 515.7
Soggetto topico: Potential theory (Mathematics)
Probabilities
Game theory
Potential Theory
Probability Theory and Stochastic Processes
Game Theory, Economics, Social and Behav. Sciences
Persona (resp. second.): MartinezServet
San MartinJaime
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Inverse M-matrices and ultrametric matrices  Visualizza cluster
ISBN: 3-319-10298-2
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910299963903321
Lo trovi qui: Univ. Federico II
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Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 2118