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Inverse M-Matrices and Ultrametric Matrices, 2014 Lecture Notes in Mathematics Series, Vol. 2118

Langue : Anglais

Auteurs :

Couverture de l’ouvrage 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 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.

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.

Provides a unified algebraic and probabilistic approach

Describes graphs and algorithms for inverse M-matrices

Gives examples and fields of applications of M-matrices

Date de parution :

Ouvrage de 236 p.

15.5x23.5 cm

Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).

Prix indicatif 36,91 €

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