ELEMENTS OF MATRIX ANALYSIS
In Chapter 10 we discussed the bivariate regression model using summation notation. In this chapter we present basic results in matrix analysis. The multiple regression model with many independent variables can be much more effectively analyzed by using vector and matrix notation. Since our goal is to familiarize the reader with basic results, we prove only those theorems which are so fundamental that the reader can learn important facts from the process of proof itself. For the other proofs we refer the reader to Bellman (1970).
Symmetric matrices play a major role in statistics, and Bellman’s discussion of them is especially good. Additional useful results, especially with respect to nonsymmetric matrices, may be found in a compact paperback volume, Marcus and Mine (1964). Graybill (1969) described specific applications in statistics. For concise introductions to matrix analysis see, for example, Johnston (1984, chapter 4), Anderson (1984, appendix), or Amemiya (1985, appendix).