E-Book Overview
The main purpose of "Linear Algebra and Linear Models" is to provide a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms are developed along the way. The book is aimed at advanced undergraduate and first year graduate master's students taking courses in linear algebra, linear models, multivariate analysis, and design of experiments. It should also be of use to research mathematicians and statisticians as a source of standard results and problems.
E-Book Content
Linear Algebra and Linear Models, Second Edition
R.B. Bapat
Springer
Preface
The main purpose of the present monograph is to provide a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary prerequisites in matrices, multivariate normal distribution, and distribution of quadratic forms are developed along the way. The monograph is primarily aimed at advanced undergraduate and first-year master’s students taking courses in linear algebra, linear models, multivariate analysis, and design of experiments. It should also be of use to research workers as a source of several standard results and problems. Some features in which we deviate from the standard textbooks on the subject are as follows. We deal exclusively with real matrices, and this leads to some nonconventional proofs. One example is the proof of the fact that a symmetric matrix has real eigenvalues. We rely on ranks and determinants a bit more than is done usually. The development in the first two chapters is somewhat different from that in most texts. It is not the intention to give an extensive introduction to matrix theory. Thus, several standard topics such as various canonical forms and similarity ar