Bilinear Forms and Zonal Polynomials

Download or read book Bilinear Forms and Zonal Polynomials written by Arak M. Mathai and published by Springer Science & Business Media. This book was released on 1995-05-19 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with bilinear forms in real random vectors and their generalizations. The authors show how zonal polynomials may be used to analyze such forms and thus to apply these concepts in a variety of statistical settings. Assuming a graduate-level background in statistics, this account is self-contained and each chapter concludes with exercises making the book ideal for a researcher seeking a straight-forward introduction to this topic. Chapter 1 covers preliminaries including a treatment of the Jacobians of matrix transformation and chapter 2 then introduces bilinear forms in Gaussian random real vectors. Chapter 3 covers quadratic forms in elliptically contoured and spherically symmetric vectors whilst chapters 4 and 5 introduce and then apply the theory of zonal polynomials to the theory of distributions of generalized quadratic and bilinear forms.