Combined matrix of diagonally equipotent matrices

Abstract

Let C(A)=A∘A−T{\mathcal{C}}\left(A)=A\circ {A}^{-T} be the combined matrix of an invertible matrix AA, where ∘\circ means the Hadamard product of matrices. In this work, we study the combined matrix of a nonsingular matrix, which is an HH-matrix whose comparison matrix is singular. In particular, we focus on C(A){\mathcal{C}}\left(A) when AA is diagonally equipotent, and we study whether C(A){\mathcal{C}}\left(A) is an HH-matrix and to which class it belongs. Moreover, we give some properties on the diagonal dominance of these matrices and on their comparison matrices.

Keywords

• h-matrix
• combined matrix
• irreducibility
• diagonally equipotent matrix
• 15a15
• 15a99
• 15b99