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Inverse M-Matrices and Ultrametric Matrices

Author: Claude Dellacherie

Publisher: Springer

Published: 2014-11-14

Total Pages: 241

ISBN-13: 3319102982

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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.

Book Synopsis Inverse M-Matrices and Ultrametric Matrices by : Claude Dellacherie

Download or read book Inverse M-Matrices and Ultrametric Matrices written by Claude Dellacherie and published by Springer. This book was released on 2014-11-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generalized Ultrametric Matrices - a Class of Inverse M-matrices

Author: Reinhard Nabben

Publisher:

Published: 1994

Total Pages: 24

ISBN-13:

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Book Synopsis Generalized Ultrametric Matrices - a Class of Inverse M-matrices by : Reinhard Nabben

Download or read book Generalized Ultrametric Matrices - a Class of Inverse M-matrices written by Reinhard Nabben and published by . This book was released on 1994 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Matrix Positivity

Author: Charles R. Johnson

Publisher: Cambridge University Press

Published: 2020-10

Total Pages: 223

ISBN-13: 1108478719

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This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.

Book Synopsis Matrix Positivity by : Charles R. Johnson

Download or read book Matrix Positivity written by Charles R. Johnson and published by Cambridge University Press. This book was released on 2020-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.

Nonnegative Matrices in the Mathematical Sciences

Author: Abraham Berman

Publisher: SIAM

Published: 1994-01-01

Total Pages: 357

ISBN-13: 0898713218

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Mathematics of Computing -- Numerical Analysis.

Book Synopsis Nonnegative Matrices in the Mathematical Sciences by : Abraham Berman

Download or read book Nonnegative Matrices in the Mathematical Sciences written by Abraham Berman and published by SIAM. This book was released on 1994-01-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Combinatorial Matrix Theory

Author: Richard A. Brualdi

Publisher: Birkhäuser

Published: 2018-03-31

Total Pages: 219

ISBN-13: 3319709534

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This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Book Synopsis Combinatorial Matrix Theory by : Richard A. Brualdi

Download or read book Combinatorial Matrix Theory written by Richard A. Brualdi and published by Birkhäuser. This book was released on 2018-03-31 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Matrix Iterative Analysis

Author: Richard S Varga

Publisher: Springer Science & Business Media

Published: 2009-12-05

Total Pages: 363

ISBN-13: 3642051561

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This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.

Book Synopsis Matrix Iterative Analysis by : Richard S Varga

Download or read book Matrix Iterative Analysis written by Richard S Varga and published by Springer Science & Business Media. This book was released on 2009-12-05 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.

Group Inverses of M-Matrices and Their Applications

Author: Stephen J. Kirkland

Publisher: CRC Press

Published: 2012-12-18

Total Pages: 330

ISBN-13: 1439888590

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Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas.

Book Synopsis Group Inverses of M-Matrices and Their Applications by : Stephen J. Kirkland

Download or read book Group Inverses of M-Matrices and Their Applications written by Stephen J. Kirkland and published by CRC Press. This book was released on 2012-12-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas.

Building Bridges between Soft and Statistical Methodologies for Data Science

Author: Luis A. García-Escudero

Publisher: Springer Nature

Published: 2022-08-24

Total Pages: 421

ISBN-13: 3031155092

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Nowadays, data analysis is becoming an appealing topic due to the emergence of new data types, dimensions, and sources. This motivates the development of probabilistic/statistical approaches and tools to cope with these data. Different communities of experts, namely statisticians, mathematicians, computer scientists, engineers, econometricians, and psychologists are more and more interested in facing this challenge. As a consequence, there is a clear need to build bridges between all these communities for Data Science. This book contains more than fifty selected recent contributions aiming to establish the above referred bridges. These contributions address very different and relevant aspects such as imprecise probabilities, information theory, random sets and random fuzzy sets, belief functions, possibility theory, dependence modelling and copulas, clustering, depth concepts, dimensionality reduction of complex data and robustness.

Book Synopsis Building Bridges between Soft and Statistical Methodologies for Data Science by : Luis A. García-Escudero

Download or read book Building Bridges between Soft and Statistical Methodologies for Data Science written by Luis A. García-Escudero and published by Springer Nature. This book was released on 2022-08-24 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, data analysis is becoming an appealing topic due to the emergence of new data types, dimensions, and sources. This motivates the development of probabilistic/statistical approaches and tools to cope with these data. Different communities of experts, namely statisticians, mathematicians, computer scientists, engineers, econometricians, and psychologists are more and more interested in facing this challenge. As a consequence, there is a clear need to build bridges between all these communities for Data Science. This book contains more than fifty selected recent contributions aiming to establish the above referred bridges. These contributions address very different and relevant aspects such as imprecise probabilities, information theory, random sets and random fuzzy sets, belief functions, possibility theory, dependence modelling and copulas, clustering, depth concepts, dimensionality reduction of complex data and robustness.

Advanced Studies in Behaviormetrics and Data Science

Author: Tadashi Imaizumi

Publisher: Springer Nature

Published: 2020-04-17

Total Pages: 472

ISBN-13: 9811527008

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This book focuses on the latest developments in behaviormetrics and data science, covering a wide range of topics in data analysis and related areas of data science, including analysis of complex data, analysis of qualitative data, methods for high-dimensional data, dimensionality reduction, visualization of such data, multivariate statistical methods, analysis of asymmetric relational data, and various applications to real data. In addition to theoretical and methodological results, it also shows how to apply the proposed methods to a variety of problems, for example in consumer behavior, decision making, marketing data, and social network structures. Moreover, it discuses methodological aspects and applications in a wide range of areas, such as behaviormetrics; behavioral science; psychology; and marketing, management and social sciences. Combining methodological advances with real-world applications collected from a variety of research fields, the book is a valuable resource for researchers and practitioners, as well as for applied statisticians and data analysts.

Book Synopsis Advanced Studies in Behaviormetrics and Data Science by : Tadashi Imaizumi

Download or read book Advanced Studies in Behaviormetrics and Data Science written by Tadashi Imaizumi and published by Springer Nature. This book was released on 2020-04-17 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the latest developments in behaviormetrics and data science, covering a wide range of topics in data analysis and related areas of data science, including analysis of complex data, analysis of qualitative data, methods for high-dimensional data, dimensionality reduction, visualization of such data, multivariate statistical methods, analysis of asymmetric relational data, and various applications to real data. In addition to theoretical and methodological results, it also shows how to apply the proposed methods to a variety of problems, for example in consumer behavior, decision making, marketing data, and social network structures. Moreover, it discuses methodological aspects and applications in a wide range of areas, such as behaviormetrics; behavioral science; psychology; and marketing, management and social sciences. Combining methodological advances with real-world applications collected from a variety of research fields, the book is a valuable resource for researchers and practitioners, as well as for applied statisticians and data analysts.

Asymptotic Properties of Permanental Sequences

Author: Michael B. Marcus

Publisher: Springer Nature

Published: 2021-03-30

Total Pages: 114

ISBN-13: 3030694852

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This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains. The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups. The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains.

Book Synopsis Asymptotic Properties of Permanental Sequences by : Michael B. Marcus

Download or read book Asymptotic Properties of Permanental Sequences written by Michael B. Marcus and published by Springer Nature. This book was released on 2021-03-30 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains. The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups. The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains.