Bilinear Forms and Zonal Polynomials (Lecture Notes in Statistics, 102)

Mathai, Arak M.; Provost, Serge B.; Hayakawa, Takesi

ISBN 10: 0387945229 / ISBN 13: 9780387945224

Published by Springer, 1995

About this Item

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Bibliographic Details

• Title: Bilinear Forms and Zonal Polynomials (Lecture Notes in Statistics, 102)
• Publisher: Springer
• Publication Date: 1995
• Language: English
• ISBN 10: 0387945229
• ISBN 13: 9780387945224
• Binding: Soft cover
• Condition: good

About this title

Synopsis

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.