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

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  • Rafael Bru
  • Maria T. Gassó
  • Isabel Giménez
  • José A. Scott

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.

Suggested Citation

  • Rafael Bru & Maria T. Gassó & Isabel Giménez & José A. Scott, 2015. "The Hadamard Product of a Nonsingular General H-Matrix and Its Inverse Transpose Is Diagonally Dominant," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-6, June.
    • Handle: RePEc:hin:jnljam:264680
    DOI: 10.1155/2015/264680
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