ABSTRACT
The aim of this book is to provide a guide to elementary matrix algebra sufficient for undertaking intermediate and advanced statistical courses such as multivariate data analysis and linear models. Starting from a definition of a matrix and covering the basic rules of addition, subtraction, multiplication and inversion, the later topics include determinants, calculation of eigenvectors and eigenvalues and differentiation of linear and quadratic forms with respect to vectors. These later topics are sometimes not included in basic courses on linear algebra but are virtually essential for full discussion of statistical topics in multivariate analysis and linear models. The notes go a little beyond meeting just this need, providing an initial guide to more advanced topics such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices. This is to provide a second step for those who need to go a little further than standard lecture courses on advanced statistics, for example, when embarking on a dissertation. As well as describing the basics of matrix algebra, including numerical calculations “by hand”, for example, of matrix multiplication and inversion, the notes give guidance on how to do numerical calculations in R (R Core Team 2014). R is broadly similar in operation to the package Matlab® but oriented specifically towards statistical applications rather than more general areas of applied mathematics. R is an open source system and is available free. It is closely similar to the commercial package S-Plus: the prime difference is that R is command-line driven without the standard menus and dialogue boxes for statistical operations in S-Plus. Otherwise, most code written for the two systems is interchangeable. There are however a few differences, for example there may be differences in the available optional arguments for some functions. Generally, all options available in S-Plus are also available in R but not necessarily vice versa. These are quickly verified by use of the help system. The sites from which R and associated software (extensions and libraries) and manuals can be found are listed at https://www.ci.tuwien.ac.at/R/mirrors.html.
