03957nam 22007095 450 991029996390332120200630202528.03-319-10298-210.1007/978-3-319-10298-6(CKB)3710000000306107(SSID)ssj0001386562(PQKBManifestationID)11994472(PQKBTitleCode)TC0001386562(PQKBWorkID)11374161(PQKB)11601247(DE-He213)978-3-319-10298-6(MiAaPQ)EBC6283558(MiAaPQ)EBC5578070(Au-PeEL)EBL5578070(OCoLC)895958791(PPN)183094336(EXLCZ)99371000000030610720141114d2014 u| 0engurnn#008mamaatxtccrInverse M-Matrices and Ultrametric Matrices[electronic resource] /by Claude Dellacherie, Servet Martinez, Jaime San Martin1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (X, 236 p. 14 illus.)Lecture Notes in Mathematics,0075-8434 ;2118Bibliographic Level Mode of Issuance: Monograph3-319-10297-4 Includes bibliographical references and index.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.Lecture Notes in Mathematics,0075-8434 ;2118Potential theory (Mathematics)ProbabilitiesGame theoryPotential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Game Theory, Economics, Social and Behav. Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13011Potential theory (Mathematics).Probabilities.Game theory.Potential Theory.Probability Theory and Stochastic Processes.Game Theory, Economics, Social and Behav. Sciences.515.7Dellacherie Claudeauthttp://id.loc.gov/vocabulary/relators/aut54847Martinez Servetauthttp://id.loc.gov/vocabulary/relators/autSan Martin Jaimeauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299963903321Inverse M-matrices and ultrametric matrices1388061UNINA