Selected Matrix Algebra Topics and Results

Abstract

Before we can begin to tackle the inference problems described near the end of the previous chapter, we must first develop an adequate working knowledge of matrix algebra useful for linear models. That is the objective of this chapter. Admittedly, the topics and results selected for inclusion here are severely abridged, being limited almost exclusively to what will actually be needed in later chapters. Furthermore, for some of the results (particularly those that are used only once or twice in the sequel), little context is provided. For much more thorough treatments of matrix algebra useful for linear models and other areas of statistics, we refer the reader to the books by Harville (J Am Stat Assoc 72:320–338, 1977) and Schott (Matrix analysis for statistics, 3rd ed. Wiley, Hoboken, 2016). In fact, for proofs not given in this chapter, we provide a reference to a proof given in one or both of those books.