Inverse M-Matrices and Ultrametric Matrices

Nonfiction, Science & Nature, Mathematics, Vector Analysis, Statistics
Cover of the book Inverse M-Matrices and Ultrametric Matrices by Claude Dellacherie, Servet Martinez, Jaime San Martin, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Claude Dellacherie, Servet Martinez, Jaime San Martin ISBN: 9783319102986
Publisher: Springer International Publishing Publication: November 14, 2014
Imprint: Springer Language: English
Author: Claude Dellacherie, Servet Martinez, Jaime San Martin
ISBN: 9783319102986
Publisher: Springer International Publishing
Publication: November 14, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Synthesis and Application of Organoboron Compounds by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Application of FPGA to Real‐Time Machine Learning by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book The Origins of Democracy in Tribes, City-States and Nation-States by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Most-Cited Scholars in Criminology and Criminal Justice, 1986-2010 by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Urban Sustainability: Policy and Praxis by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Population Aging, Fertility and Social Security by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Programming and Performance Visualization Tools by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Energy in Australia by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Manual of Neonatal Respiratory Care by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Cybersecurity in Israel by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Software Developers as Users by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Clinician’s Guide to Breastfeeding by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Plant Epigenetics by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Women's Networks in Medieval France by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Foundations of Hardware IP Protection by Claude Dellacherie, Servet Martinez, Jaime San Martin
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy