Usually, the Gauss-Markov Theorem is stated in terms of the properties of 
. For a geometrical interpretation, it is convenient to make an
equivalent statement in terms of the fitted vector 
, which appears
in the geometry of OLS. There is no substantive difference. After all, the
two have a one-to-one relationship whenever 
is well-defined:
If X is full column rank, then
Here is a statement of the theorem.
We give a proof of this theorem in Proof of the Gauss-Markov Theorem
. The proof is stated in terms of projections. All linear unbiased
estimators of 
are projections of the vector y.
