Inverse M-matrices and ultrametric matrices / Claude Dellacherie, Servet Martinez and Jaime San Martin.
Material type:
TextSeries: Lecture notes in mathematics ; 2118.Publication details: New York : Springer, 2014.Description: x, 236 p. ; illustrationsISBN: - 9783319102979
- 512.9434 23 D357
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 512.9434 D357 (Browse shelf(Opens below)) | Available | 135848 |
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| 512.9434 C967 Matrices and linear transformations | 512.9434 D263 Mathematics of matrices: a first book of matrix theory and linear algebra | 512.9434 D324 Random matrix theory | 512.9434 D357 Inverse M-matrices and ultrametric matrices / | 512.9434 D855 Sparse matrices and their uses | 512.9434 D855 Direct method for sparse matrices | 512.9434 Ea11 Some contributions to generalized inverses and the linear complementarity problem |
Includes index.
1. Introduction--
2. Inverse m-matrices and potentials --
3. Ultrametric Matrices --
4. Graph of Ultrametric Type Matrices --
5. Filtered Matrices --
6. Hadamard Functions of Inverse m-matrices --
A Beyond Matrices --
B Basic Matrix Block Formulae --
C Symbolic Inversion of a Diagonally Dominant m- matrices --
Index of Notations --
Index.
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.
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