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Nonnegativity of Schur complements of nonnegative idempotent matrices

Please always quote using this URN:urn:nbn:de:0296-matheon-5091
  • Let $A$ be a nonnegative idempotent matrix. We show 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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Metadaten
Author:Shmuel Friedland, Elena Virnik
URN:urn:nbn:de:0296-matheon-5091
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/04/22
Release Date:2008/04/22
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A09 Matrix inversion, generalized inverses
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A15 Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
Preprint Number:505
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