02417nmm a2200349 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002400139245013100163250001700294260005600311300004000367505034500407653001600752653002300768653001600791653003500807653002100842653001800863700003100881700003200912041001900944989003600963490003300999028003001032856007201062082001101134520092201145EB000901493EBX0100000000000000069806400000000000000.0cr|||||||||||||||||||||141202 ||| eng a97833191029861 aDellacherie, Claude00aInverse M-Matrices and Ultrametric MatriceshElektronische Ressourcecby Claude Dellacherie, Servet Martinez, Jaime San Martin a1st ed. 2014 aChambSpringer International Publishingc2014, 2014 aX, 236 p. 14 illusbonline resource0 aInverse 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 aGame Theory aProbability Theory aGame theory aPotential theory (Mathematics) aPotential Theory aProbabilities1 aMartinez, Servete[author]1 aSan Martin, Jaimee[author]07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aLecture Notes in Mathematics50a10.1007/978-3-319-10298-640uhttps://doi.org/10.1007/978-3-319-10298-6?nosfx=yxVerlag3Volltext0 a515.96 aThe 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