Let the General Linear Model be represented by
y = Xß + u u ~ N(0,σ2I)
where X is n x p non-stochastic and of rank p and let ß = (XtX)-1Xty be the OLS estimate of ß.
Now suppose that certain linear constraints are known to hold between various elements of the parameter vector ß, i.e. there is a p x k matrix R and a k x 1 vector q such that Rtß = q, where k < p. Determine the Least Squares estimator of ß if the usual sum of squared residuals (y - Xß)t(y - Xß) is minimised with the added constraints that Rtß = q.