The Hadamard Product of a Nonsingular General H‐Matrix and Its Inverse Transpose Is Diagonally Dominant

Rafael Bru, Maria T. Gassó, Isabel Giménez and José A. Scott

Journal of Applied Mathematics, 2015, vol. 2015, issue 1

Abstract: We study the combined matrix of a nonsingular H‐matrix. These matrices can belong to two different H‐matrices classes: the most common, invertible class, and one particular class named mixed class. Different results regarding diagonal dominance of the inverse matrix and the combined matrix of a nonsingular H‐matrix belonging to the referred classes are obtained. We conclude that the combined matrix of a nonsingular H‐matrix is always diagonally dominant and then it is an H‐matrix. In particular, the combined matrix in the invertible class remains in the same class.

Date: 2015
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https://doi.org/10.1155/2015/264680

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2015:y:2015:i:1:n:264680

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