Stability criteria for matrices (Q1298273)

Two classes of matrices are considered: strictly diagonally dominant ones -- with \(|a_{ii}|>\sum_{j\neq i}|a_{ij}|\) -- and generalized strictly dominant ones -- those matrices \(A\) for which a positive diagonal matrix \(X\) exists such that \(AX\) is strictly diagonally dominant. For these classes simple criteria for stability exist. Consequently the paper gives various sufficient conditions for strictly diagonal dominance and generalized strictly diagonal dominance.