1. Any strictly diagonally dominant matrix is trivially a weakly chained diagonally dominant matrix. 2. Any strictly diagonally dominant matrix is trivially a weakly chained diagonally dominant matrix. 3. This segment consists of strictly diagonally dominant ( thus nonsingular ) matrices, except maybe for A. 4. These are irreducible matrices that are weakly diagonally dominant , but strictly diagonally dominant in at least one row. 5. These are irreducible matrices that are weakly diagonally dominant, but strictly diagonally dominant in at least one row. 6. Weakly chained diagonally dominant matrices are nonsingular and include the family of " irreducibly diagonally dominant " matrices. 7. Weakly chained diagonally dominant matrices are nonsingular and include the family of " irreducibly diagonally dominant " matrices. 8. *PM : Properties of diagonally dominant matrix, id = 7483-- WP guess : Properties of diagonally dominant matrix-- Status: 9. *PM : Properties of diagonally dominant matrix, id = 7483-- WP guess : Properties of diagonally dominant matrix-- Status: 10. This amounts to assuming that \ mathbf J _ \ sigma is diagonally dominant and solving the k th equation only for the k unknown.