Inverse M-Matrices and Ultrametric Matrices (Lecture Notes in Mathematics, 2118) - Softcover

Dellacherie, Claude; Martinez, Servet; San Martin, Jaime

 
9783319102979: Inverse M-Matrices and Ultrametric Matrices (Lecture Notes in Mathematics, 2118)
Softcover
ISBN 10: 3319102974 ISBN 13: 9783319102979
Publisher: Springer, 2014

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2014
Language
English
ISBN 10 
3319102974
ISBN 13 
9783319102979
Binding
Paperback
Number of pages
246