Matrix Algebra From a Statistician's Perspective
Matrix algebra plays a very important role in statistics and in many other dis- plines. In many areas of statistics, it has become routine to use matrix algebra in thepresentationandthederivationorveri?cationofresults. Onesuchareaislinear statistical models; another is multivariate analysis. In these areas, a knowledge of matrix algebra isneeded in applying important concepts, as well as instudying the underlying theory, and is even needed to use various software packages (if they are to be used with con?dence and competence). On many occasions, I have taught graduate-level courses in linear statistical models. Typically, the prerequisites for such courses include an introductory (- dergraduate) course in matrix (or linear) algebra. Also typically, the preparation provided by this prerequisite course is not fully adequate. There are several r- sons for this. The level of abstraction or generality in the matrix (or linear) algebra course may have been so high that it did not lead to a “working knowledge” of the subject, or, at the other extreme, the course may have emphasized computations at the expense of fundamental concepts. Further, the content of introductory courses on matrix (or linear) algebra varies widely from institution to institution and from instructor to instructor. Topics such as quadratic forms, partitioned matrices, and generalized inverses that play an important role in the study of linear statistical models may be covered inadequately if at all.
Provides the background in matrix algebra necessary to do research and understand the results in these areas
Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices
Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions"
This book offers thorough and unified coverage of the fundamental concepts of matrix algebra. Its approach will make it particularly suited to those with an interest in statistics or related disciplines. But it does much more, too: it is enlightening in specialized areas of statistics such as linear statistical models and multivariate analysis. David Harville, a former associate editor of the Journal of the American Statistical Association, ensures that the style and level of presentation make the contents accessible to a broad audience. It includes a number of very useful results that have, up to now, only been available from relatively obscure sources, and for which detailed proofs are provided. It also contains numerous exercises, the solutions to which can be found in the author’s Matrix Algebra: Exercises and Solutions.