Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Inverse M-matrices and ultrametric matrices / Claude Dellacherie, Servet Martinez and Jaime San Martin.

By: Contributor(s): Material type: TextTextSeries: Lecture notes in mathematics ; 2118.Publication details: New York : Springer, 2014.Description: x, 236 p. ; illustrationsISBN:
  • 9783319102979
Subject(s): DDC classification:
  • 512.9434 23 D357
Contents:
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.
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Holdings
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
Total holds: 0

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.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in