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.
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 |