Inverse M-Matrices and Ultrametric Matrices
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Publication
2014 - Springer London, Limited
Language
English
Word Count
59,000 words, Guess
Page Count
236 pages
Identifiers
- ISBN-139783319102986
- ISBN-103319102982
- Better World Books9783319102986
- Open LibraryOL34520495M
Classifications
- LCCQA1-939
Description
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.
Subjects
Other Editions
- Inverse M-Matrices and Ultrametric Matrices
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