Restrictions and Generalized Inverses in Linear Models
S. R. Searle · The American Statistician · 1984
Given any generalized inverse (X'X)− appropriate to normal equations X'Xb 0 = X'y for the linear model y = Xb + e, a procedure is given for obtaining from it a generalized inverse appropriate to a restricted model having restrictions P'b = 0 for P'b nonestimable.