Geodesic
Nonnegativity of Schur complements of nonnegative idempotent matrices
The electronic journal of linear algebra, Tome 17 (2008), pp. 426-435.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let A be a nonnegative idempotent matrix. It is shown that the Schur complement of a submatrix, using the Moore-Penrose inverse, is a nonnegative idempotent matrix if the submatrix has a positive diagonal. Similar results for the Schur complement of any submatrix of A are no longer true in general.
Classification : 15A09, 15A15, 15A48
Keywords: nonnegative idempotent matrices, Schur complement, Moore-Penrose inverse, generalized inverse 
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     author = {Friedland, Shmuel and Virnik, Elena},
     title = {Nonnegativity of {Schur} complements of nonnegative idempotent matrices},
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Friedland, Shmuel; Virnik, Elena. Nonnegativity of Schur complements of nonnegative idempotent matrices. The electronic journal of linear algebra, Tome 17 (2008), pp. 426-435. http://geodesic.mathdoc.fr/item/ELA_2008__17__a15/