| 000 | 04850cam a2200745 i 4500 | ||
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| 001 | ocn895958791 | ||
| 003 | OCoLC | ||
| 005 | 20250703133350.0 | ||
| 006 | m o d | ||
| 007 | cr cnu|||||||| | ||
| 008 | 141118s2014 sz a ob 001 0 eng d | ||
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| 020 | _z9783319102979 | ||
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| 024 | 7 |
_a10.1007/978-3-319-10298-6 _2doi |
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| 037 | _bSpringer | ||
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_a512.9/434 _223 |
| 049 | _aMAIN | ||
| 100 | 1 |
_aDellacherie, Claude, _eauthor. _1https://id.oclc.org/worldcat/entity/E39PBJgCMVYfMkkDqg69BcVDMP _973562 |
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| 245 | 1 | 0 |
_aInverse m-matrices and ultrametric matrices / _cClaude Dellacherie, Servet Martinez, Jaime San Martin. |
| 264 | 1 |
_aCham [Switzerland] : _bSpringer, _c[2014] |
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| 300 |
_a1 online resource (x, 236 pages) : _billustrations |
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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 | ||
| 347 | _bPDF | ||
| 490 | 1 |
_aLecture notes in mathematics, _x1617-9692 ; _v2118 |
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| 504 | _aIncludes bibliographical references and index. | ||
| 588 | 0 | _aOnline resource; title from PDF title page (SpringerLink, viewed November 19, 2014). | |
| 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. | ||
| 546 | _aEnglish. | ||
| 650 | 0 |
_aMatrices. _91156 |
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| 650 | 0 |
_aInverse problems (Differential equations) _99305 |
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| 650 | 6 |
_aMatrices. _91156 |
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| 650 | 6 | _aProblèmes inverses (Équations différentielles) | |
| 650 | 7 |
_aMatrices (Matemáticas) _2embne _9974084 |
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| 650 | 7 |
_aInverse problems (Differential equations) _2fast _99305 |
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| 650 | 7 |
_aMatrices _2fast _91156 |
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| 700 | 1 |
_aMartínez, Servet, _eauthor. _1https://id.oclc.org/worldcat/entity/E39PBJkHkdKDGdyCrhJVfTxxDq _979108 |
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| 700 | 1 |
_aSan Martín, Jaime, _eauthor. _1https://id.oclc.org/worldcat/entity/E39PCjF3Qfh3t6ypF4VbtRrMGd _979109 |
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| 758 |
_ihas work: _aInverse M-matrices and ultrametric matrices (Text) _1https://id.oclc.org/worldcat/entity/E39PCGTgHqpFMRfq8KMBh3PQD3 _4https://id.oclc.org/worldcat/ontology/hasWork |
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| 776 | 0 | 8 |
_iPrinted edition: _z9783319102979 |
| 830 | 0 |
_aLecture notes in mathematics (Springer-Verlag) ; _v2118. |
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| 856 | 4 | 0 | _uhttps://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-319-10298-6 |
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