Inverse MMatrices and Ultrametric Matrices
The study of Mmatrices, their inverses and discrete potential theory is now a wellestablished part of linear algebra and the theory of Markov chains. The main focus of this monograph is the socalled inverse Mmatrix problem, which asks for a characterization of nonnegative matrices whose inverses...
Main Authors:  , , 

Format:  eBook 
Language:  English 
Published: 
Cham
Springer International Publishing
2014, 2014

Edition:  1st ed. 2014 
Series:  Lecture Notes in Mathematics

Subjects:  
Online Access:  
Collection:  Springer eBooks 2005  Collection details see MPG.ReNa 
Summary:  The study of Mmatrices, their inverses and discrete potential theory is now a wellestablished part of linear algebra and the theory of Markov chains. The main focus of this monograph is the socalled inverse Mmatrix problem, which asks for a characterization of nonnegative matrices whose inverses are Mmatrices. We present an answer in terms of discrete potential theory based on the ChoquetDeny Theorem. A distinguished subclass of inverse Mmatrices 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 Mmatrices are developed and probabilistic insights are provided throughout the monograph 

Physical Description:  X, 236 p. 14 illus online resource 
ISBN:  9783319102986 