Inverse m-matrices and ultrametric matrices / Claude Dellacherie, Servet Martinez, Jaime San Martin.

By:

Dellacherie, Claude [author.]

Contributor(s):

Material type: Text

TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2118.Publisher: Cham [Switzerland] : Springer, [2014]Description: 1 online resource (x, 236 pages) : illustrationsContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783319102986
3319102982

Subject(s):

Additional physical formats: Printed edition:: No titleDDC classification:

512.9/434 23

LOC classification:

QA188 .D45 2014eb

Online resources:

Click here to access online

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.

Summary: 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.

Holdings ( 1 )
Title notes ( 5 )

Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
eBook	e-Library	eBook LN Mathematic		Available

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Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed November 19, 2014).

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.

English.