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.
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Bru et al. (2009) studied this question.
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