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

الملخص EN

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.