Prerequisites

Abstract

This chapter presents some definitions and results frequently used throughout this book. The purpose is first of all to establish the notation, therefore the presentation is at times short and compact. Apart from notation this chapter also contains an important interpretation of the direct product of two complex matrices, and we define the direct product of two complex vector spaces. Further we consider a real isomorphism between a p-dimensional complex vector space and a 2p-dimensional real vector space. This isomorphism is based on considering a complex vector space as a real vector space. Next we study the concepts of complex random variables, vectors and matrices. Besides definitions of those we regard the expectation, variance and covariance operators individually for each case. Both definitions and properties for the operators are considered. We also define the characteristic function of a complex random variable and of a complex random vector. We see that a characteristic function determines a distribution uniquely. Finally mutual independence of complex random vectors is defined.