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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Dellacherie, Claude (Autor), Martinez, Servet (Autor), San Martin, Jaime (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edición:1st ed. 2014.
Colección:Lecture Notes in Mathematics, 2118
Temas:
Potential theory (Mathematics).
Probabilities.
Game theory.
Potential Theory.
Probability Theory.
Game Theory.
Acceso en línea:Texto Completo

MARC

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100 1 |a Dellacherie, Claude.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Inverse M-Matrices and Ultrametric Matrices  |h [electronic resource] /  |c by Claude Dellacherie, Servet Martinez, Jaime San Martin. 
250 |a 1st ed. 2014. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2014. 
300 |a X, 236 p. 14 illus.  |b online resource. 
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490 1 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2118 
505 0 |a 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. 
520 |a 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. 
650 0 |a Potential theory (Mathematics). 
650 0 |a Probabilities. 
650 0 |a Game theory. 
650 1 4 |a Potential Theory. 
650 2 4 |a Probability Theory. 
650 2 4 |a Game Theory. 
700 1 |a Martinez, Servet.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a San Martin, Jaime.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319102993 
776 0 8 |i Printed edition:  |z 9783319102979 
830 0 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2118 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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