The general linear model and the generalized singular value decomposition

AbstractA new derivation is given for the generalized singular value decomposition of two matrices X and F having the same number of rows. It is shown how this decomposition reveals the structure of the general Gauss-Markov linear model (y, Xβ, σ2FF′), and exhibits the structure and solution of the generalized linear least squares problem used to provide the best linear unbiased estimator for the model. The decomposition is used to prove optimality of the estimator and to reveal the structure of the covariance matrix of the error of the estimator