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＜電子ブック＞
Inverse M-Matrices and Ultrametric Matrices / by Claude Dellacherie, Servet Martinez, Jaime San Martin
(Lecture Notes in Mathematics. ISSN:16179692 ; 2118)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	X, 236 p. 14 illus : online resource
著者標目	*Dellacherie, Claude author Martinez, Servet author San Martin, Jaime author SpringerLink (Online service)
件　名	LCSH:Potential theory (Mathematics) LCSH:Probabilities LCSH:Game theory FREE:Potential Theory FREE:Probability Theory FREE:Game Theory
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-10298-6

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