Diagonal dominance and invertibility of matrices

Abstract

A weakly diagonally dominant matrix may or may not be invertible. We characterize, in terms of combinatorial structure and sign pattern when such a matrix is invertible, which is the common case. Examples are given.

Keywords

• cycle lengths
• invertibility
• matrices of odd (even) type
• (weak) diagonal dominance
• 15a15
• 15b51
• 15a09