A square matrix is diagonally dominant when the absolute value of every diagonal entry is at least the sum of the absolute values of the other entries in its row.
A matrix is strictly diagonally dominant when every diagonal-dominance inequality is strict. A real symmetric strictly diagonally dominant matrix with positive diagonal is positive definite by the Gershgorin circle theorem.
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A diagonally dominant matrix is a square matrix in which each diagonal element is greater than the sum of the absolute values of all the other elements in the corresponding row.