Preliminaries

Abstract

Linear algebra is used extensively throughout this book and those topics particularly relevant to the development in this monograph are given within the chapters; other results are given in the Appendix. References to the Appendix are labeled with a prefix “A”, for example A.3 is theorem 3 in the Appendix. Vectors and matrices are denoted by boldface letters a and A, respectively, and scalars are denoted by italics. For example, a = (a _i ) is a vector with ith element a _i and A = (a _ij ) is a matrix with i, jth element a _ij . I shall use the same notation with random variables, because using uppercase for random variables and lowercase for their values can cause confusion with vectors and matrices. We endeavor, however, to help the reader by using the lower case letters in the latter half of the alphabet, namely u, v, …, z, with the occasional exception (because of common usage) for random variables and the rest of the alphabet for constants. All vectors and matrices contain real elements, that is belong to $\mathbb{R}$, and we denote n-dimensional Euclidean space by $\mathbb{R}^{n}$.