A new approach to the concept of a strong unified-least-squares matrix (Q1883301)

A very interesting result on the invariance of the expression \(\mathcal{R}(AB^-C) \subseteq \mathcal{R}(D)\) for every generalized inverse \(B^-\) (i.e., \(BB^-B=B\)) is developed. This result is used in the statistical problem of defining, from two different view points, the strong unified-least-squares for the general Gauss-Markov model showing that both are equivalent. Finally, all matrices appearing in those equivalent definitions are characterized.