For a given general linear model ℳ={y,Xβ,Σ}, we investigate relationships between the best linear unbiased estimations (BLUEs) under its two transformed models ℳ1={Ay,AXβ,AΣA′} and ℳ2={By,BXβ,BΣB′}. We first establish some expansion formulas for calculating the ranks and inertias...