Diagonally dominant matrix

In mathematics, a square matrix is said to be diagonally dominant if, for every row of the matrix, the magnitude of the diagonal entry in a row is greater than or equal to the sum of the magnitudes of all the other (off-diagonal) entries in that row. More precisely, the matrix A {\displaystyle A} is diagonally dominant if | a i i | ≥ ∑ j ≠ i | a i j | ∀ i {\displaystyle |a_{ii}|\geq \sum _{j\neq i}|a_{ij}|\ \ \forall \ i} where a i j {\displaystyle a_{ij}} denotes the entry in the i {\displaystyle i} th row and j {\displaystyle j} th column.

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