9 Introduction of Matrix Algebra and Linear Models

9.1 Multiple Regression

9.1.1 An application to multivariate selection

9.2 Elementary Matrix Algebra

9.2.1 Basic notation

9.2.2 Partitioned matrices

9.2.3 Addition and subtraction

9.2.4 Multiplication

9.2.5 Transposition

9.2.6 Inverses and solutions to systems of equations

9.2.7 Determinants and minors

9.2.8 Computing inverses

9.3 Expectations of Random Vectors and Matrices

9.4 Covariance Matrices of Transformed Vectors

9.5 The Multivariate Normal Distribution

9.5.1 Properties of the MVN

9.6 Overview of Linear Models

9.6.1 Ordinary Least squares

9.6.2 Generalized least squares