Nonnegativity of Schur complements of nonnegative idempotent matrices

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Shmuel Friedland
Elena Virnik

Abstract

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.

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