The paper provides a projector based approach to the best linear unbiased estimator (BLUE). By revisiting the so called generalized projection operator, introduced in Rao (J R Slat Soc Set B Slat Methodol 36:442-448, 1974), a number of new formulae for BLUE is established. Furthermore, some attention is paid to the coincidence of the BLUE and the ordinary least squares estimator.