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