Arak M Mathai's Books

Bilinear Forms and Zonal Polynomials

By: Arak M. Mathai,Serge B. Provost,Takesi Hayakawa

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Bilinear Forms and Zonal Polynomials

By: Arak M. Mathai,Serge B. Provost,Takesi Hayakawa

The book deals with bilinear forms in real random vectors and their generalizations as well as zonal polynomials and their applications in handling generalized quadratic and bilinear forms. The book is mostly self-contained. It starts from basic principles and brings the readers to the current research level in these areas. It is developed with detailed proofs and illustrative examples for easy readability and self-study. Several exercises are proposed at the end of the chapters. The complicated topic of zonal polynomials is explained in detail in this book. The book concentrates on the theoretical developments in all the topics covered. Some applications are pointed out but no detailed application to any particular field is attempted. This book can be used as a textbook for a one-semester graduate course on quadratic and bilinear forms and/or on zonal polynomials. It is hoped that this book will be a valuable reference source for graduate students and research workers in the areas of mathematical statistics, quadratic and bilinear forms and their generalizations, zonal polynomials, invariant polynomials and related topics, and will benefit statisticians, mathematicians and other theoretical and applied scientists who use any of the above topics in their areas. Chapter 1 gives the preliminaries needed in later chapters, including some Jacobians of matrix transformations. Chapter 2 is devoted to bilinear forms in Gaussian real ran dom vectors, their properties, and techniques specially developed to deal with bilinear forms where the standard methods for handling quadratic forms become complicated.

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Page Count

385

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461242428

ISBN 13

9781461242420

Multivariate Statistical Analysis in the Real and Complex Domains

By: Arak M. Mathai,Serge B. Provost,Hans J. Haubold

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Multivariate Statistical Analysis in the Real and Complex Domains

By: Arak M. Mathai,Serge B. Provost,Hans J. Haubold

This book explores topics in multivariate statistical analysis, relevant in the real and complex domains. It utilizes simplified and unified notations to render the complex subject matter both accessible and enjoyable, drawing from clear exposition and numerous illustrative examples. The book features an in-depth treatment of theory with a fair balance of applied coverage, and a classroom lecture style so that the learning process feels organic. It also contains original results, with the goal of driving research conversations forward. This will be particularly useful for researchers working in machine learning, biomedical signal processing, and other fields that increasingly rely on complex random variables to model complex-valued data. It can also be used in advanced courses on multivariate analysis. Numerous exercises are included throughout.

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Page Count

939

Publisher

Springer Nature

Published Date

ISBN 10

3030958647

ISBN 13

9783030958640

Matrix Methods And Fractional Calculus

By: Arak M Mathai,Hans J Haubold

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Matrix Methods And Fractional Calculus

By: Arak M Mathai,Hans J Haubold

Fractional calculus in terms of mathematics and statistics and its applications to problems in natural sciences is NOT yet part of university teaching curricula. This book is one attempt to provide an approach to include topics of fractional calculus into university curricula. Additionally the material is useful for people who do research work in the areas of special functions, fractional calculus, applications of fractional calculus, and mathematical statistics.

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Page Count

291

Publisher

World Scientific

Published Date

ISBN 10

9813227540

ISBN 13

9789813227545

Probability and Statistics

A Course for Physicists and Engineers

By: Arak M. Mathai,Hans J. Haubold

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Probability and Statistics

A Course for Physicists and Engineers

By: Arak M. Mathai,Hans J. Haubold

This book offers an introduction to concepts of probability theory, probability distributions relevant in the applied sciences, as well as basics of sampling distributions, estimation and hypothesis testing. As a companion for classes for engineers and scientists, the book also covers applied topics such as model building and experiment design. Contents Random phenomena Probability Random variables Expected values Commonly used discrete distributions Commonly used density functions Joint distributions Some multivariate distributions Collection of random variables Sampling distributions Estimation Interval estimation Tests of statistical hypotheses Model building and regression Design of experiments and analysis of variance Questions and answers

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Page Count

732

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

311056260X

ISBN 13

9783110562606

Linear Algebra

A Course for Physicists and Engineers

By: Arak M. Mathai,Hans J. Haubold

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Linear Algebra

A Course for Physicists and Engineers

By: Arak M. Mathai,Hans J. Haubold

In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to be self-contained, so no other material is required for an understanding of the topics covered. As the basis for courses on space and atmospheric science, remote sensing, geographic information systems, meteorology, climate and satellite communications at UN-affiliated regional centers, various applications of the formal theory are discussed as well. These include differential equations, statistics, optimization and some engineering-motivated problems in physics. Contents Vectors Matrices Determinants Eigenvalues and eigenvectors Some applications of matrices and determinants Matrix series and additional properties of matrices

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Page Count

564

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110562596

ISBN 13

9783110562590

Jacobians Of Matrix Transformation And Functions Of Matrix Arguments

By: Arak M Mathai

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Jacobians Of Matrix Transformation And Functions Of Matrix Arguments

By: Arak M Mathai

This book concentrates on the topic of evaluation of Jacobians in some specific linear as well as nonlinear matrix transformations, in the real and complex cases, which are widely applied in the statistical, physical, engineering, biological and social sciences. It aims to develop some techniques systematically so that anyone with a little exposure to multivariable calculus can easily follow the steps and understand the various methods by which the Jacobians in complicated matrix transformations are evaluated. The material is developed slowly, with lots of worked examples, aimed at self-study. Some exercises are also given, at the end of each section.The book is a valuable reference for statisticians, engineers, physicists, econometricians, applied mathematicians and people working in many other areas. It can be used for a one-semester graduate level course on Jacobians and functions of matrix argument.

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Page Count

449

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813105070

ISBN 13

9789813105072

Matrix Methods And Fractional Calculus

By: Arak M Mathai,Hans J Haubold

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Matrix Methods And Fractional Calculus

By: Arak M Mathai,Hans J Haubold

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Page Count

291

Publisher

World Scientific

Published Date

ISBN 10

9813227540

ISBN 13

9789813227545

Linear Algebra

A Course for Physicists and Engineers

By: Arak M. Mathai,Hans J. Haubold

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Linear Algebra

A Course for Physicists and Engineers

By: Arak M. Mathai,Hans J. Haubold

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Page Count

468

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110562502

ISBN 13

9783110562507

Book's by Arak M Mathai

Bilinear Forms and Zonal Polynomials

Bilinear Forms and Zonal Polynomials

Multivariate Statistical Analysis in the Real and Complex Domains

Multivariate Statistical Analysis in the Real and Complex Domains

Matrix Methods And Fractional Calculus

Matrix Methods And Fractional Calculus

Probability and Statistics

Probability and Statistics

Linear Algebra

Linear Algebra

Jacobians Of Matrix Transformation And Functions Of Matrix Arguments

Jacobians Of Matrix Transformation And Functions Of Matrix Arguments

Matrix Methods And Fractional Calculus

Matrix Methods And Fractional Calculus

Linear Algebra

Linear Algebra

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