Inverse m-matrices and ultrametric matrices /
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| Author / Creator: | Dellacherie, Claude, author. |
|---|---|
| Imprint: | Cham [Switzerland] : Springer, [2014] |
| Description: | 1 online resource (x, 236 pages) : illustrations. |
| Language: | English |
| Series: | Lecture notes in mathematics, 1617-9692 ; 2118 Lecture notes in mathematics (Springer-Verlag) ; 2118. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11089764 |
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| 100 | 1 | |a Dellacherie, Claude, |e author. |0 http://id.loc.gov/authorities/names/n82152813 |1 http://viaf.org/viaf/2469153 | |
| 245 | 1 | 0 | |a Inverse m-matrices and ultrametric matrices / |c Claude Dellacherie, Servet Martinez, Jaime San Martin. |
| 264 | 1 | |a Cham [Switzerland] : |b Springer, |c [2014] | |
| 300 | |a 1 online resource (x, 236 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Lecture notes in mathematics, |x 1617-9692 ; |v 2118 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed November 19, 2014). | |
| 505 | 0 | |a Inverse 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 | |a The 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 | |a Matrices. |0 http://id.loc.gov/authorities/subjects/sh85082210 | |
| 650 | 0 | |a Inverse problems (Differential equations) |0 http://id.loc.gov/authorities/subjects/sh85067684 | |
| 650 | 7 | |a Inverse problems (Differential equations) |2 fast |0 (OCoLC)fst00978098 | |
| 650 | 7 | |a Matrices. |2 fast |0 (OCoLC)fst01012399 | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Martínez, Servet, |e author. |0 http://id.loc.gov/authorities/names/n89669827 |1 http://viaf.org/viaf/24677734 | |
| 700 | 1 | |a San Martín, Jaime, |e author. |0 http://id.loc.gov/authorities/names/n2002015659 |1 http://viaf.org/viaf/29837675 | |
| 710 | 2 | |a SpringerLink (Online service) |0 http://id.loc.gov/authorities/names/no2005046756 |1 http://viaf.org/viaf/148105729 | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319102979 |
| 830 | 0 | |a Lecture notes in mathematics (Springer-Verlag) ; |v 2118. | |
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