Discussion
A \(n \times n\) matrix A is diagonally dominant of :
Answer: A
A is diagonally dominant if each diagonal entry's absolute value is at least the sum of the absolute values of the other entries in its row.
In symbols, \(|a_{ii}| \ge \sum_{j \neq i} |a_{ij}|\) for every row i (strict dominance asks for \(\gt\)). This is the condition that guarantees convergence of the Jacobi and Gauss-Seidel iterations.
Being the largest entry in the row is weaker: in the row (3, 2, 2), 3 is the largest but 3 < 4. Comparing values without absolute values can be satisfied by large negative off-diagonal entries, which defeats the purpose. Zero diagonal entries are the opposite of dominance.
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