The Moore–Penrose inverse of a partitioned nonnegative definite matrix Original Research Article

Consider an arbitrary symmetric nonnegative definite matrix A and its Moore–Penrose inverse A+, partitioned, respectively asExplicit expressions for G1, G2 and G4 in terms of E, F and H are given. Moreover, it is proved that the generalized Schur complement (A+/G4)=G1−G2G4+G2′ is always below the Moore–Penrose inverse (A/H)+ of the generalized Schur complement (A/H)=E−FH+F′ with respect to the Löwner partial ordering.