This book is developed as a reference book for theoretical as well as applied statisticians. Those belonging to the latter group will find the examples very useful and should be able to make good use of the results. A large number of unpublished results are included in Chapters 3, 4, 5 and 6. Most of the results included in this monograph are proved; in some cases an outline of the proof and a reference containing the complete proof are provided. Many of the proofs require a good understanding of basic statistical principles as well as a thorough background in mathematics. Those who have specialized in other fields such as engineering and econometrics will also find a number of results relevant to their own disciplines.
This book can also be used as a textbook for a one semester graduate course on quadratic forms in random variables for students specializing in mathematical statistics or in multivariate analysis. To this end a number of worked examples are included in Chapters 3, 4, and 5 and a good number of results are given in the form of exercises at the end of those chapters and Chapter 6.