On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model

Equality and proportionality of the ordinary least-squares estimator (OLSE), the weighted least-squares estimator (WLSE), and the best linear unbiased estimator (BLUE) for XβXβ in the general linear (Gauss–Markov) model M={y,Xβ,σ2Σ}M={y,Xβ,σ2Σ} are investigated through the matrix rank method.