## Journal of Applied Mathematics

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

#### 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.

#### Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 264680, 6 pages.

Dates
First available in Project Euclid: 17 August 2015

https://projecteuclid.org/euclid.jam/1439816403

Digital Object Identifier
doi:10.1155/2015/264680

Mathematical Reviews number (MathSciNet)
MR3356663

#### Citation

Bru, Rafael; Gassó, Maria T.; Giménez, Isabel; Scott, José A. The Hadamard Product of a Nonsingular General H-Matrix and Its Inverse Transpose Is Diagonally Dominant. J. Appl. Math. 2015 (2015), Article ID 264680, 6 pages. doi:10.1155/2015/264680. https://projecteuclid.org/euclid.jam/1439816403

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