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