2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76346A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.Functional Analysis46C07, 47A62, 46C05Weighted generalized inverses, oblique projections and least squares problemstext