= Diagonal dominance
A square <matrix> $A$ has row <diagonal dominance> when $|a_{ii}|\geq\sum_{j\ne i}|a_{ij}|$ in every row. <Strict diagonal dominance> requires a strict inequality in every row. Strictness guarantees nonsingularity, and a positive margin gives the <inverse infinity-norm bound from diagonal dominance>. Weak <diagonal dominance> alone does not: the <matrix> $\left(\begin{smallmatrix}1&-1\\-1&1\end{smallmatrix}\right)$ has <diagonal dominance> but has the nonzero <kernel> <vector> $(1,1)^T$.
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