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 The Real Numbers by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book A Casebook in Interprofessional Ethics by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Evolution of the Protein Synthesis Machinery and Its Regulation by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Myelodysplastic Syndromes by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Australian Screen in the 2000s by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Masculinity, Labour, and Neoliberalism by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Global Challenges and the Emerging World Order by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Electroweak Symmetry Breaking by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Information and Communication Technologies in Education, Research, and Industrial Applications by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Fear and Uncertainty in Europe by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Model-Based Safety and Assessment by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Advances in Time Series Analysis and Forecasting by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Concise Dictionary of Engineering by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Cyber-Humans by Claude Dellacherie, Servet Martinez, Jaime San Martin
Cover of the book Taxation of Income from Domestic and Cross-border Collective Investment 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