000 | 03450nam a22005175i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/978-3-319-10298-6 _2doi |
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050 | 4 | _aQA404.7-405 | |
072 | 7 |
_aPBWL _2bicssc |
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072 | 7 |
_aMAT033000 _2bisacsh |
|
072 | 7 |
_aPBWL _2thema |
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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. |
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300 |
_aX, 236 p. 14 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |