Weakly chained diagonally dominant matrix

In mathematics, the weakly chained diagonally dominant matrices are a family of nonsingular matrices that include the strictly diagonally dominant matrices.

We say row ${\displaystyle i}$ of a complex matrix ${\displaystyle A=(a_{ij})}$ is strictly diagonally dominant (SDD) if ${\displaystyle |a_{ii}|>\textstyle {\sum _{j\neq i}}|a_{ij}|}$. We say ${\displaystyle A}$ is SDD if all of its rows are SDD. Weakly diagonally dominant (WDD) is defined with ${\displaystyle \geq }$ instead.

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