2009•Numerical Linear Algebra with ApplicationsOpen access

Schur complement of general H‐matrices

Rafael Bru, C. Corral, I. Giménez, J. Mas

Abstract

Abstract It is well known that the Schur complement of some H‐matrices is an H‐matrix. In this paper, the Schur complement of any general H‐matrix is studied. In particular, it is proved that the Schur complement, if it exists, is an H‐matrix and the class to which the Schur complement belongs is studied. In addition, results are given for singular irreducible H‐matrices and for the Schur complement of nonsingular irreducible H‐matrices. Copyright © 2009 John Wiley & Sons, Ltd.

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Key concepts: Schur complement, Schur's theorem, Mathematics, Schur product theorem, Complement (music), Schur's lemma, Schur decomposition, Invertible matrix