Estimability of linear parametric functions in a one-dimensional linear model

In the general linear model Ey=Xξ, the vector Cξ is estimable whenever there exists a matrix L such that ELy=Cξ. Several characterizations of estimability are presented. The haracterizations concern matrix and rank equalities based on X and XX′.  Moreover, usefulness of such characterizations is discussed from a computational point of view. For new results on this subject see a paper by I. S. Alalouf and G. P. H. Styan