The BLUE of X{J can be obtained by taking T =

V + XX'. Prove this by showing that

(a) C(X) C C(T) if and only if TT-X = X and

(b) if T = V + XX', then TT- X = X.

Hint: Searle and Pukelsheim (1987) base a proof of

(b) on 0= (J - TT-)T(J - TT-)' = (J - TT-)V(J - TT-Y

+ (J - TT-)XX'(I - TT-Y and the fact that the last term is the sum of two nonnegative definite matrices.