Nonnegativity of Schur complements of nonnegative idempotent matrices
Shmuel Friedland, Elena Virnik · Electronic Journal of Linear Algebra · 2008
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.