LEADER 03957nam 22007095 450 001 9910299963903321 005 20200630202528.0 010 $a3-319-10298-2 024 7 $a10.1007/978-3-319-10298-6 035 $a(CKB)3710000000306107 035 $a(SSID)ssj0001386562 035 $a(PQKBManifestationID)11994472 035 $a(PQKBTitleCode)TC0001386562 035 $a(PQKBWorkID)11374161 035 $a(PQKB)11601247 035 $a(DE-He213)978-3-319-10298-6 035 $a(MiAaPQ)EBC6283558 035 $a(MiAaPQ)EBC5578070 035 $a(Au-PeEL)EBL5578070 035 $a(OCoLC)895958791 035 $a(PPN)183094336 035 $a(EXLCZ)993710000000306107 100 $a20141114d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aInverse M-Matrices and Ultrametric Matrices$b[electronic resource] /$fby Claude Dellacherie, Servet Martinez, Jaime San Martin 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (X, 236 p. 14 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2118 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-10297-4 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThe study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2118 606 $aPotential theory (Mathematics) 606 $aProbabilities 606 $aGame theory 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 615 0$aPotential theory (Mathematics). 615 0$aProbabilities. 615 0$aGame theory. 615 14$aPotential Theory. 615 24$aProbability Theory and Stochastic Processes. 615 24$aGame Theory, Economics, Social and Behav. Sciences. 676 $a515.7 700 $aDellacherie$b Claude$4aut$4http://id.loc.gov/vocabulary/relators/aut$054847 702 $aMartinez$b Servet$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSan Martin$b Jaime$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299963903321 996 $aInverse M-matrices and ultrametric matrices$91388061 997 $aUNINA