Let the General Linear Model be represented by

y = X + u u ~ N(0,σ2I)

where X is n x p non-stochastic and of rank p and let = (XtX)-1Xty be the OLS estimate of .

Now suppose that certain linear constraints are known to hold between various elements of the parameter vector , i.e. there is a p x k matrix R and a k x 1 vector q such that Rt = q, where k < p. Determine the Least Squares estimator of if the usual sum of squared residuals (y - X)t(y - X) is minimised with the added constraints that Rt = q.