The Moore-Penrose inverse of a partitioned nonnegative definite matrix. Groß, J. *Linear Algebra and its Applications*, 321(1-3):113–121, Elsevier, 2000. doi abstract bibtex 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.

@Article{ Gros_2000aa,
abstract = { 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.},
author = {Groß, Jürgen},
doi = {10.1016/S0024-3795(99)00073-7},
file = {Gros_2000aa.pdf},
issn = {0024-3795},
journal = {Linear Algebra and its Applications},
keywords = {schur,linear-systems,matrix-algebra},
langid = {english},
number = {1-3},
pages = {113--121},
publisher = {Elsevier},
title = {The Moore-Penrose inverse of a partitioned nonnegative definite matrix},
volume = {321},
year = {2000},
shortjournal = {Lin. Algebra. Appl.}
}

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