Of course, for proofs of these results the reader will have to refer to the original source. I want to re-emphasize that this is a book about linear models. It is not traditional multivariate analysis, time series, or geostatistics. Multivariate linear models are viewed as linear models with a nondiagonal covariance matrix. Discriminant analysis is related to the Mahalanobis distance and multivariate analysis of variance.
Principle components are best linear predictors.
Frequency domain time series involves linear models with a peculiar design matrix. Time domain analysis involves models that are linear in the parameters but have random design matrices. While other approaches to these problems may yield different insights, there is value in having a unified approach to looking at these problems. Developing such a unified approach is the purpose of this book. There are two well known models with linear structure that are conspicuous by their absence in my two volumes on linear models.