文档介绍：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 distribu-
tion 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 are not found
here. We often derive only those results that are explicitly used later. The list of
facts in matrix theory that are elementary, elegant, but not covered here is almost
endless.
We put a great deal of emphasis on the generalized inverse and its applications.
This amounts to avoiding the “geometric” or the “projections” approach that is
favored by some authors and taking recourse to a more algebraic approach. Partly
as a personal bias, I feel that the geometric approach works well in providing an
vi Preface
understanding of why a result should be true but has limitations when es to
proving the result rigorously.
The first three chapters are devoted to matrix theory, linear estimation, and tests
of linear hypotheses, respectively. Chapter 4 collects several results on eigenv