000 03450nam a22005175i 4500
001 978-3-319-10298-6
003 DE-He213
005 20190213151457.0
007 cr nn 008mamaa
008 141114s2014 gw | s |||| 0|eng d
020 _a9783319102986
_9978-3-319-10298-6
024 7 _a10.1007/978-3-319-10298-6
_2doi
050 4 _aQA404.7-405
072 7 _aPBWL
_2bicssc
072 7 _aMAT033000
_2bisacsh
072 7 _aPBWL
_2thema
082 0 4 _a515.96
_223
100 1 _aDellacherie, Claude.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aInverse M-Matrices and Ultrametric Matrices
_h[electronic resource] /
_cby Claude Dellacherie, Servet Martinez, Jaime San Martin.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aX, 236 p. 14 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2118
505 0 _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.
520 _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.
650 0 _aPotential theory (Mathematics).
650 0 _aDistribution (Probability theory.
650 0 _aMathematics.
650 1 4 _aPotential Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12163
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aGame Theory, Economics, Social and Behav. Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13011
700 1 _aMartinez, Servet.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSan Martin, Jaime.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319102993
776 0 8 _iPrinted edition:
_z9783319102979
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2118
856 4 0 _uhttps://doi.org/10.1007/978-3-319-10298-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10813
_d10813