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Bilinear Forms and Zonal Polynomials

  • A. M. Mathai
  • Serge B. Provost
  • Takesi Hayakawa

Part of the Lecture Notes in Statistics book series (LNS, volume 102)

Table of contents

  1. Front Matter
    Pages i-xii
  2. A. M. Mathai, Serge B. Provost, Takesi Hayakawa
    Pages 1-16
  3. A. M. Mathai, Serge B. Provost, Takesi Hayakawa
    Pages 17-87
  4. A. M. Mathai, Serge B. Provost, Takesi Hayakawa
    Pages 89-162
  5. A. M. Mathai, Serge B. Provost, Takesi Hayakawa
    Pages 163-246
  6. A. M. Mathai, Serge B. Provost, Takesi Hayakawa
    Pages 247-318
  7. Back Matter
    Pages 319-378

About this book

Introduction

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.

Keywords

Likelihood Normal distribution binomial correlation statistics

Authors and affiliations

  • A. M. Mathai
    • 1
  • Serge B. Provost
    • 2
  • Takesi Hayakawa
    • 3
  1. 1.Department of MathematicsMcGill UniversityMontrealCanada
  2. 2.Department of Statistical and Actuarial SciencesUniversity of Western OntarioLondonCanada
  3. 3.Department of EconomicsHitotubashi UniversityTokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4242-0
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94522-4
  • Online ISBN 978-1-4612-4242-0
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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