Inverse M-Matrices and Ultrametric Matrices

• Main Authors: Dellacherie, Claude (Author), Martinez, Servet (Author), San Martin, Jaime (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Lecture Notes in Mathematics, 2118
• Subjects: Mathematics.; Potential theory (Mathematics).; Game theory.; Probabilities.; Potential Theory.; Probability Theory and Stochastic Processes.; Game Theory, Economics, Social and Behav. Sciences.

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...

Table of Contents:

• 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.