Introduction

In this chapter, most of the notation used in this book will be introduced. It is not assumed that the reader is familiar with topics such as Kronecker product, Hadamard product, or vectorization operator. Therefore, this chapter defines these concepts and gives some of their properties. The current chapter also provides background material for matrix manipulations that will be used later in the book. However, it contains just the minimum of material that will be used later because many excellent books in linear algebra are available for the reader to consult (Gantmacher 1959a-1959b; Horn & Johnson 1985; Strang 1988; Magnus & Neudecker 1988; Golub & van Loan 1989; Horn & Johnson 1991; Lütkepohl 1996; Harville 1997; Bernstein 2005).

This chapter is organized as follows: Section 2.2 introduces the basic notation and classification used for complex-valued variables and functions. A discussion of the differences between analytic and non-analytic functions is presented in Section 2.3. Basic matrix-related definitions are provided in Section 2.4. Several results involving matrix manipulations used in later chapters are found in Section 2.5. Section 2.6 offers exercises related to the material included in this chapter. Theoretical derivations and computer programming in MATLAB are topics of these exercises.